2.01 - Time Value of Money - Problems

Question 1

As part of the negotiations for the sale of a cottage property, a potential buyer offers Raymond, the vendor of the property, $10,000 payable four years after the deal closes. Raymond must calculate the present value of the future payment in order to make an informed decision. Assume an annual nominal interest rate of 10%, compounded annually.

Answer 1

$6,830.13 invested today at 10% would grow to $10,000 in four years.

Question 2

Harriett has just leased a new car that her brother-in-law has agreed to purchase from her for $12,000 at the end of the five-year lease period. Using an annual interest assumption of 7%, compounded annually, calculate the present value of the $12,000 that Harriett will receive in five years.

Answer 2

Harriett explains to her brother-in-law that, using a 7% annual interest rate, she can consider the $12,000 received after five years to be equivalent to $8,555.83 today.

Question 3

As part of the payment for the purchase of her business, Donna is offered a promissory note for $135,000, which is due at the end of two years. Assuming an annual return of 6%, compounded annually, what is the present value of this promissory note?

Answer 3

The present value of Donna’s promissory note is $120,149.52.

Question 4

Tiffany has received an offer from a corporation that wants to buy her company for $3,500,000, payable in full after 18 months. Tiffany wonders what the $3,500,000 offer represents in today’s dollars. Assuming an annual return of 9%, compounded annually, calculate the present value of the offer.

Answer 4

The present value of the offer Tiffany has received is $3,075,588.99.

Question 5

Ashley received a $1,000 investment certificate from her great aunt on her 12th birthday. The certificate pays a 3% annual interest rate, compounded once each year, and matures on her 27th birthday. What is the maturity value of Ashley’s investment certificate?

Answer 5

Ashley’s investment certificate will be worth $1,557.97 at maturity, when she turns 27.

Question 6

Sheila’s parents deposited $500,000 into an account on her 22nd birthday, but she is unable to access the funds until her 30th birthday. The account in which the money sits pays an annual interest rate of 8%, compounded once each year. How much will Sheila’s investment be worth when she reaches her 30th birthday?

Answer 6

Sheila’s investment will be worth $925,465.11 on her 30th birthday.

Question 7

Liam, age 55, has been offered a retirement package that includes a $50,000 settlement, payable today. If Liam accepts the offer, he would like to invest this lump- sum amount for the next five years and then use the money towards the purchase of an annuity. If Liam receives an annual interest rate of 8%, compounded annually, for each of the next five years, how much will he have accumulated?

Answer 7

Liam will have $73,466.40 to use towards the purchase of an annuity.

Question 8

Anthony has been asked to calculate the future value of three scenarios. Each has the same present value, but has a different interest rate and investment period. Which scenario has the greatest future value? (Disregard taxes.): Option A - $100,000, invested for 3.5 years at an annual interest rate of 23.3%, compounded quarterly; Option B - $100,000, invested for seven years at an annual interest rate of 12%, compounded annually; Option C - $100,000, invested for 18 years at an annual interest rate of 4.4%, compounded monthly. There are three answers to this question.

Answer 8

The results are $220,920.43 for Option A, $221,068.14 for Option B and $220,461.20 for Option C. While close, Option B results in the highest future value.

Question 9

What is the present value of a periodic payment stream that a) provides Raymond with $2,500 at the end of each year for the next four years, assuming that the interest rate is 10%, compounded annually; b) a payment of $2,500 at the beginning of each period, rather than at the end of each period (same assumptions); and c) assuming a monthly payment of $208.33 at the beginning of each month (same assumptions).

Answer 9

The value of the periodic payment streams are a) $7,924.66 b) $8,717.13 c) $8,282.52.

Question 10

Alfred would like to set up an account to pay his grandson $5,000 at the end of each year for the next 25 years. Using an interest assumption of 5%, compounded annually, how much should Alfred invest today?

Answer 10

Alfred must invest $70,469.72 to meet his objective.

Question 11

Billy has a $13,000 student loan. He has approached his parents, asking them to pay off the loan now and offering to pay them back at a rate of $1,200 at the end of each year for the next 15 years. Billy’s parents feel he must accept some financial responsibility, so they would like to charge him an annual interest rate of 5%, compounded once each year. Using these assumptions, determine if the present value of Billy’s payback proposal results in the full repayment of $13,000 to his parents.

Answer 11

The stream of payments that Billy proposed has a present value of $12,455.59, compared with the $13,000 that Billy’s parents must pay now.

Question 12

As part of her retirement package, Nelly expects to receive $6,000 at the beginning of each quarter, for the next 15 years. Assuming an annual 7% return, compounded quarterly, what is the present value of this stream of payments?

Answer 12

Based on the assumptions, Nelly’s retirement package is equivalent to receiving $225,665.13 today.

Question 13

Gail has received an annuity that pays her $10,000 at the beginning of each year for 12 years. Gail would like to sell it now in the open market for its fair market value (FMV). Assuming an annual interest rate of 6.5%, compounded annually, calculate the present value to determine what the payment stream represented by the annuity is worth today.

Answer 13

The present value of this future revenue stream is $86,890.42.

Question 14

Robert would like to purchase a 20-year annuity that pays him $4,000 at the beginning of each year. Payments would begin immediately. Assuming an annual interest rate of 7.2%, compounded annually, how much would the annuity cost Robert?

Answer 14

The annuity would cost Robert $44,729.47.

Question 15

Shiam has an investment that pays her $200 at the beginning of each month. There are exactly four years of payments remaining, after which there is no value. Assuming an annual interest rate of 6.6%, compounded monthly, what is the present value of Shiam’s payment stream?

Answer 15

Shiam’s payment stream has a present value of $8,463.41.

Question 16

Wilson plans to save $6,000 at the end of every year for the nine years remaining before he retires. He believes he can achieve an annual return of 4.4%, compounded annually. How much will Wilson have when he reaches retirement? Wilson also wonders what effect it would have on his total savings if he sold his motorcycle now for $7,800 and deposited the money in the same account. There are two answers to this question.

Answer 16

At the end of nine years, Wilson will have accumulated $64,547.06 and by adding the proceeds from the disposition of his motorcycle to the account at the beginning, Wilson’s investment accumulates to $76,039.15 at retirement.

Question 17

Bob and Carol feel it is important to begin saving now for their children’s university costs. They estimate they have 11 years to save $50,000. After meeting all of the expenses of daily living, Bob and Carol believe they can save $196.78 at the end of each month. They expect to achieve an annual return of 7.1%, compounded monthly. Will this savings pattern achieve the $50,000 their children need?

Answer 17

Unfortunately, the savings pattern Bob and Carol have developed will fall well short of their savings target, achieving only $39,199.75, compared with a need of $50,000.

Question 18

Jay wants to raise the money required to make a balloon payment of $63,000 at the end of a 7.5-year period. He currently has $12,300 in an account into which he is making monthly payments of $342 at the beginning of each month. He anticipates that he can earn an annual interest rate of 8%, compounding monthly. Jay wonders if he will have enough money to cover his balloon payment in 7.5 years.

Answer 18

Jay is happy to discover that, based on the assumptions and if everything goes according to plan, he will have $64,636.16 in 7.5 years, which is slightly more than the $63,000 he needs.

Question 19

At the beginning of each month, Rachel will receive a licensing fee of $856 from clients who use software she has just finished developing. Rachel wants to sell the underlying intellectual property, but only after she has accumulated enough money from her licensing fee revenue and the interest she earns on that fund. Her target is to sell the intellectual property in four years. If Rachel can earn an annual investment return of 3.8%, based on monthly compounding, how much will she have accumulated at the end of four years? And if Rachel’s goal is to have accumulated $60,000 before she sells the intellectual property, how much time will it take her to reach that goal?

Answer 19

Based on the assumptions, Rachel will have accumulated $44,439.82 after four years and will meet her goal of $60,000 in 5.27 years (63.22 months).

Question 20

How much will Mahood accumulate if he opens an account with a $16,212 deposit, adds $112.91 at the beginning of each month for 5.75 years, and earns an annual return of 9%, compounded monthly?

Answer 20

Mahood will accumulate $37,380.38 after 5.75 years.

Question 21

Ian, a high school teacher, wants to demonstrate to his class the power of compound interest. He explains that an individual who deposits $100 at the beginning of each month for the next 55 years into an investment paying 7.6% annual interest, compounded monthly, will accumulate a very large amount. How much exactly will this investment accumulate?

Answer 21

Based on these assumptions, after 55 years, the individual will have $1,009,139.15.

Question 22

If Heba deposits $1,000 at the beginning of every year for seven years into an account with an initial balance of $1,000, what is the value of her account at the end of seven years? Assume that she earns a return of 2.5%, compounded annually.

Answer 22

At the end of seven years, Heba will have $8,924.80 in the account.

Question 23

A bank account pays a 3% annual nominal interest rate, compounded monthly. What is the annual effective interest rate?

Answer 23

The annual effective interest rate (EFF) is 3.04%.

Question 24

An investment certificate pays 6.7% annual nominal interest rate, compounded daily. What is the annual effective interest rate?

Answer 24

The annual effective interest rate (EFF) is 6.93%.

Question 25

Dorothy’s bank manager explains that the annual effective interest rate on her bank account is 3.9%. If the compounding period is quarterly, what is the annual nominal interest rate?

Answer 25

The annual nominal interest rate (NOM) is 3.84%.

Question 26

Mark invests $1,000 in an account and, at the end of six years, he has accumulated a total of $1,500. Assuming interest is compounded annually, what annual nominal interest rate did he receive to produce an account balance of $1,500?

Answer 26

Mark’s $1,000 investment earned an annual nominal interest rate of 6.99%, compounded annually, over the six-year holding period.

Question 27

Stefanie invests $150 in mutual funds at the end of each month for five years. At the end of the five years, her investment has accumulated to $12,400. Assuming monthly compounding, what annual nominal return did the investment earn?

Answer 27

Stefanie earned an annual nominal return of 12.45% during the five years.

Question 28

Steve started with an initial balance of $12,500 in an investment and added $200 at the end of each month for 3.5 years. Assuming monthly compounding, if his balance is $22,875 at the end of the period, what annual nominal rate of return did Steve earn? What annual effective rate of return did Steve earn? There are two answers to this question.

Answer 28

Steve earned an annual nominal rate of return of 3.23% and an annual effective rate of return is 3.28% (rounded) on the investment over 3.5 years.

Question 29

Colleen has saved $2,000 towards the purchase of a car that she would like to buy in four years. Colleen can save $375 at the end of each month, and she needs $22,800 to pay for the car. What annual nominal rate of return does she need to earn, based on monthly compounding?

Answer 29

Colleen needs to earn an annual nominal return of 5.95% to achieve her goal.

Question 30

Ruth has agreed to lend her best friend John $5,000, and he has agreed to repay her $1,200 at the end of each year for the next five years. Based on this schedule of payments, what annual nominal interest rate is Ruth charging John on the loan?

Answer 30

Ruth is charging her friend an annual nominal interest rate of 6.4%, compounded annually.

Question 31

To buy equipment for his shop, Max is borrowing $32,000 right now. He plans to repay the debt over six years, at which time the equipment will no longer be of value to him, so he plans to sell it for $8,000. If Max makes monthly payments of $519 at the end of each month for six years, and gives the $8,000 residual value to the lender at the end of the six years, what annual nominal interest rate is he paying? If the lender offered to lower the monthly payment to $489 to close the deal, what annual nominal interest rate would Max be paying? There are two answers to this question.

Answer 31

Max is paying an annual nominal interest rate of 10.41% on the first deal and an annual nominal interest rate of 8.8% on the negotiated deal.

Question 32

Barbara is seeking a $15,000 loan on which she plans to make $400 payments at the end of each month for five years, after which the loan will be fully repaid. What annual nominal interest rate is she paying? What about annual effective interest rate? There are two answers to this question.

Answer 32

Barbara is paying an annual nominal interest rate of 20.3% and an annual effective interest rate of 22.31%.

Question 33

Monique financed the cost of her education by making a payment at the beginning of each month for 3.75 years to her uncle, who prepaid her $12,000 tuition fees. Her uncle wants a 7% annual return, compounded monthly, on the money he paid on her behalf. Calculate the monthly payments Monique must make to her uncle.

Answer 33

Monique’s monthly payments are $302.21.

Question 34

Tompkin Enterprises needs $25,000,000 at the end of 10 years to construct a facility. If the company can earn an annual return of 5.8%, compounded annually, how much does it need to save at the end of each year to have $25,000,000 at the end of 10 years?

Answer 34

Tompkin Enterprises must save $1,914,586.79 every year for 10 years to accumulate the $25,000,000 it needs at the end of 10 years.

Question 35

Tony wants to buy a car, but he would like to save up the cash before making the purchase. He feels he can earn an annual rate of return of 6.9%, compounded annually, and would like to accumulate sufficient funds over a five-year period. Tony figures he will need $27,800 at the end of five years to purchase the car and currently has savings of $10,500. What amount does Tony need to save at the end of each year if he wants to have sufficient funds to purchase the car?

Answer 35

Under this scenario, Tony needs to save $2,289.82 each year to meet his $27,800 target.

Question 36

Baha works for a company that allows employees to deduct a portion of their monthly paycheque to fund a sabbatical year at some time in the future. Baha’s employer pays 3% interest, compounded monthly, on this deducted money. Baha, who currently earns $84,000 annually, wants to accumulate an amount equal to two-thirds of his present salary to fund his sabbatical year, which will begin in five years. How much does Baha need to instruct his employer to deduct from his monthly paycheque during the next five years, if he is to accumulate the required amount by the beginning of his sabbatical? Assume that the monthly deduction is made at the end of each month.

Answer 36

Baha needs to deduct $866.25 from his month-end pay to accumulate $56,000 by the beginning of his sabbatical year.

Question 37

Calculate the investment required, at the end of each month, to generate $50,000 by the end of five years, assuming a 5.5% annual rate of return, compounded monthly.

Answer 37

With these assumptions, monthly investments of $725.89 will generate $50,000 by the end of five years.

Question 38

Karen and Daryl are considering a tropical vacation that will cost $5,500. Although they do not have the money on hand, they know they can borrow from Karen’s parents if they agree to pay the loan back within two years. If the couple plans to pay an annual interest rate of 2.75%, compounded monthly, how much must they repay at the beginning of each month?

Answer 38

Karen and Daryl must make monthly payments of $235.25, under this scenario.

Question 39

Xavier earned $3,500 this summer working as a camp counsellor. He wants to buy a new road bicycle with this money. He invested the $3,500 in a short-term savings account that earns 4% compounded annually. The road bicycle Xavier wants costs $6,000. How long will it take for Xavier’s summer earnings to grow to $6,000?

Answer 39

It will take 13.74 years for Xavier’s summer earnings to grow to $6,000.

Question 40

Ru wants to buy a car. She expects to be able to buy a good-quality used car for $25,000. She has not set aside anything yet for the purchase, but is able to save $600 at the end of each month. How long will it take Ru to save enough to buy a car if she earns a nominal rate of 6%, compounded monthly?

Answer 40

Ru will save enough to buy a car in 37.94 months, which is equivalent to three years and nearly two months.

Question 41

Aesha inherited $32,000 from her grandfather. She would like to buy a Recreational Vehicle (RV) with the money to travel across Canada. However, $32,000 is not enough money. She needs $88,000 to purchase the RV of her dreams. If Aesha invests her inheritance in a savings account that pays an annual nominal rate of 5.5%, compounded monthly, and she contributes $800 at the end of each month, when will she have enough money to buy her RV?

Answer 41

It will take Aesha 52.46 months, or 4 years and 4.46 months, to save enough to buy her RV.

Question 42

Pierre is 45 years old and has saved only $32,000 for his retirement. He has determined that he needs $1,000,000 in retirement savings to fund his desired lifestyle. He can save $1,200 at the beginning of each month towards his retirement goal. How many years will it be before he can retire if his retirement savings and his monthly contributions are invested at a rate of 6% per year, compounded monthly?

Answer 42

Pierre can retire in 303.48 months, or 25.29 years (25 years and 3.5 months).

Question 43

Sangeeta is 65 years old and retires tomorrow. She has $275,000 in retirement savings and wants to receive payments of $36,000 per year at the beginning of each year. How many years will it take her to run out of money if she invests her retirement savings at an annual nominal rate of 8.25%, compounded annually.

Answer 43

Sangeeta will run out of money in 11 years.

Question 44

Maddie just bought a new car and financed it with a $33,500 loan at an annual interest rate of 7.95%, compounded monthly. She pays $550 at the beginning of each month towards the loan. How long will it be before Maddie’s car loan is fully repaid?

Answer 44

Maddie’s car loan will be fully repaid in 77.6 months, or six years and 5.6 months.

Question 45

Every month, Rex deposits $169 into a bank account that offers daily compounding. The annual nominal interest rate is 4%. He wants to know what a) his bank balance will be in five years. What would his bank balance be if interest was b) compounded monthly and c) yearly? There are three answers to this question.

Answer 45

With daily compounding (and monthly payments), the future value of this payment stream is a) $11,206.36. For monthly compounding his balance would be b) $11,204.52 and for yearly compounding his balance would be c) $10,984.30.

Question 46

Marie inherited an ordinary annuity that will pay her $300 monthly for another 2.5 years. What is the present value of this ordinary annuity, assuming an annual interest rate of 4%, compounded monthly?

Answer 46

The present value of this ordinary annuity is $8,551.09.

Question 47

David has purchased an annuity due that pays $970 each year for the next 12 years, starting today (i.e., at the beginning of the period). What is the present value of this annuity due, assuming an annual interest rate of 5.3%, compounded annually?

Answer 47

The present value of this annuity due is $8,901.77.

Question 48

Joanne has a court-ordered spousal support agreement to pay her former husband $400 at the end of each month for 7.25 years. Since the payments are uniform amounts, this works exactly like an ordinary annuity. Assuming an annual interest rate of 3.9%, compounded monthly, what is the present value of Joanne’s ordinary annuity?

Answer 48

Joanne’s ordinary annuity has a present value of $30,270.30.

Question 49

Dan invests $5,000 at the beginning of each year in an account that pays 6% interest, compounded annually. What is the value of this account in 3.3 years?

Answer 49

The future value of Dan’s account is $18,728.33.

Question 50

Tom just turned 65 years old, and he has a life expectancy of 28.46 years. He is considering buying a guaranteed life annuity product that will pay him $1,500 at the beginning of each month starting on his 80th birthday. If the deferred annuity is calculated based on an annual interest rate of 4.23%, compounded monthly, how much would it cost for Tom to purchase the annuity today? (Hint - this is a “present value of a deferred periodic payment stream” question.)

Answer 50

The amount Tom requires at age 80 to purchase an annuity that provides payments beginning at age 80 and continuing for the rest of his life (13.46 years) is $185,137.36, which means it would cost Tom $98,269.50 to purchase the annuity today.

Question 51

Jane just opened an investment account. She plans to contribute $150 to the account at the end of each month until her daughter, Beth, turns 15. Beth just turned 6, and Jane intends to give her the balance in the account on her 18th birthday. If Jane can achieve a 5.2% return, compounded monthly, on the account over the full period, what amount can she give Beth on her 18th birthday? (Hint - this is a “future value of a deferred periodic payment stream” question.)

Answer 51

The amount that will have accumulated when Beth turns 15 is $20,602.51, therefore Jane could give Beth $24,072.64 on her 18th birthday, after 3 more years of compounding with no additional payments.

Question 52

Peter owns a 25-year bond with a face value of $10,000, bearing a coupon rate of 6%. The bond matures in 20 years. If the current market rate is 8%, how much would someone pay today for Peter’s bond?

Answer 52

The present value of Peter’s bond is 8,020.72.

Question 53

Joan has a 15-year bond issued with a face value of $100,000 and a coupon rate of 5%. A buyer is interested in Joan’s bond at a time when the prevailing interest rate is 3.5%; therefore, Joan expects to realize a premium on the face value of the bond. There are eight years left until the bond reaches maturity. What is the present value, or market price, of the bond?

Answer 53

Joan will realize $110,387.87 on the sale of this bond.

Question 54

Chris is considering the purchase of a bond with a $1,000,000 face value that pays a coupon rate of 6.2% and has exactly six years remaining until maturity. If Chris pays $925,000 for the bond, what is his annual nominal rate of return?

Answer 54

The annual nominal interest rate is 7.79%.

Question 55

For $642,000, Brittany purchased a bond with eight years to maturity that has a coupon rate of 4% and a face value of $600,000. What is Brittany’s annual nominal rate of interest? What is the annual effective yield? There are two answers to this question.

Answer 55

The annual nominal rate of interest is 3.0089% and the annual effective yield is 3.0315%.

Question 56

Mato, who has accumulated retirement savings of $41,000, would like to retire in 13 years. By that time, he hopes to have accumulated $100,000 in total retirement savings. He estimates that he can earn an annual return of 2.8%, compounded monthly. How much will Mato have to invest at the end of each month for the next 13 years to meet his $100,000 objective?

Answer 56

If Mato invests $218.31 at the end of each month for 13 years, he will have the $100,000 he hopes to accumulate for his retirement.

Question 57

Erica would like to retire with sufficient capital to provide a monthly retirement income of $1,500 at the end of each month. She anticipates that she will need the income for 25 years during retirement and can earn an annual rate of return of 5%, compounded monthly. How much will Erica need to fund her retirement plan?

Answer 57

Erica will need $256,590.07 to fund her retirement plan.

Question 58

Jamie is about to retire and has accumulated $429,000 in an RRSP. She would like to draw a retirement income of $3,000 at the beginning of each month for 16 years. Jamie wants to know what annual nominal interest rate she needs to earn during retirement to support her plan, assuming monthly compounding.

Answer 58

If her retirement fund earns an annual nominal interest rate of 3.91%, compounded monthly, Jamie will have sufficient capital to achieve her retirement goals.

Question 59

Jack wants to have a $500,000 retirement fund when he retires in 8.5 years. At the moment, he has $289,000 in his retirement account. He plans to contribute $750 at the end of each month for the remaining 8.5 years that he is at work. Assuming that Jack’s retirement account earns interest that compounds monthly, what annual nominal rate of interest does he need to achieve to enable him to fund his retirement goal?

Answer 59

If Jack’s retirement account earns a nominal annual return of 4.08% (or more), compounded monthly, he will achieve his goal of accumulating $500,000.

Question 60

Louise is approaching retirement age but is unsure whether she wants to retire. She has a retirement account balance of $377,000, and she would like to create an income stream of $2,500 at the end of each month. She anticipates an annual return of 4.8%, compounded monthly. Based on these assumptions, how long will Louise’s money last?

Answer 60

Louise’s retirement fund should last 231.54 months, or 19.3 years.

Question 61

Harvey approaches a credit union for a $25,000 loan to finance his new car purchase. The manager tells him that he will have to pay the debt off over five years and that his payments will be $525, at the beginning of each month. What annual nominal interest rate will Harvey pay, assuming monthly compounding?

Answer 61

Harvey will pay an annual nominal interest rate of 9.85% for his car loan. Note that in this example, the loan payment was due at the beginning of the month. However, in real life, loans are most commonly calculated on a deferred payment schedule, which means payments are due at the end of the month.

Question 62

Martin has $60,000 saved for a down payment towards a new boat. He needs to borrow funds for the balance and anticipates an annual interest rate of 6%, compounded monthly. Martin would like to pay off the debt over a five-year period and feels he can afford payments of $2,000 at the end of each month. What is the maximum loan amount Martin can afford to borrow, and what is the maximum amount Martin can pay for the boat?

Answer 62

Martin’s proposed repayment schedule supports a maximum loan amount of approximately $103,451. Add Martin’s $60,000 down payment to this maximum loan amount and he can afford to pay a maximum of $163,451 for the boat.

Question 63

Susan borrowed $19,100 from her sister for a period of 10.5 years. She promised to pay annual interest of 7.7%, compounded monthly, and to make payments at the end of each month. What is Susan’s monthly payment amount?

Answer 63

Susan’s monthly payment amount is $221.50.

Question 64

Tim has a car loan with $10,400 still outstanding, and he is paying 8% interest, compounded monthly. He would like to double his monthly payments to $500. How many months will it take for Tim to pay off the remaining balance of the loan? Assume that Tim makes payments at the end of each month.

Answer 64

If he doubles his monthly payments to $500, Tim has 22.47 monthly payments left.

Question 65

Laura leases dental equipment worth $50,000 from a finance company. The lease runs for five years. She makes monthly payments of $930 at the beginning of each month. In addition, she must make a $10,000 balloon payment at the end of the lease. What annual nominal rate of interest is Laura paying on the lease?

Answer 65

Laura is paying an annual nominal rate of interest of 10.17%.

Question 66

Thomas has an investment with a nominal interest rate of 4%, while the expected rate of inflation is 2%. If inflation runs at 2%, what is Thomas’s real rate of return?

Answer 66

Thomas’s investment has a real rate of return of 1.96%.

Question 67

Casey was quite excited to see that she could obtain a 4.75% nominal interest rate on the renewal of her investment. However, inflation was projected at 1.5% for the upcoming period. If inflation remains as expected, what real rate of return will Casey experience on her investment?

Answer 67

With an inflation rate of 1.5%, Casey’s real rate of return will be 3.2%.

Question 68

Cheryl is quite wealthy, and she would like to set aside sufficient funds to help her mother with long-term expenses. Cheryl would like to provide her mother with $20,000 in annual income for the next 25 years, payable at the beginning of each year, and indexed for annual inflation of 1.5%. Assuming Cheryl can earn a return of 6% on her investment, compounded annually, how much money does she need today to fund the annual income, payable at the beginning of each year?

Answer 68

Cheryl needs $311,843.39 to fund the desired annual income for her mother.

Question 69

Blair has invested $100,000 in a non-registered interest-bearing investment that pays an annual nominal interest rate of 5.5%, compounded annually. Blair’s marginal tax rate is 42%. What is Blair’s after-tax rate of return? What amount of after-tax income will Blair derive from this investment after one year? There are two answers to this question.

Answer 69

Blair’s after-tax rate of return is 3.19% and Blair’s after-tax income from this investment will be $3,190 at the end of the first year.

Question 70

Herbert and Myra are working with their financial planner to develop a savings program aligned with their personal retirement objectives. At retirement, they hope to have sufficient non-registered savings to provide an annual after-tax income of $60,000 for 25 years, indexed for annual inflation of 2%. If, during retirement, Herbert and Myra can earn a before-tax annual return of 7%, compounded annually, and they anticipate a 35% marginal tax rate, what savings amount do they need at the beginning of retirement? Assume they want to receive their retirement income annually, at the beginning of each year. If Herbert and Myra could earn 10% before tax, how would this affect the required savings? There are two answers to this question.

Answer 70

Herbert and Myra need savings of $1,133,099.15 to fund their current retirement plans, assuming a 7% before-tax annual return. Increasing the rate of return to 10% decreases the required savings to $937,438.75.

Question 71

Lawrence is considering buying an investment that never matures but pays $1,000 at the end of each month in perpetuity. The prevailing market nominal interest rate is 8%, compounded monthly. What should the market price of the security be?

Answer 71

The market price of the security should be $150,000.

Question 72

Harold’s brother owes him $1,000. However, instead of repaying the entire $1,000, Harold’s brother promises to repay him $5 at the beginning of each month for the rest of his life. The prevailing market nominal interest rate is 5.5%, compounded monthly. What is the present value of this perpetual?

Answer 72

The value of this perpetual is $1,095.91, which is more than the $1,000 Harold’s brother currently owes him.

Question 73

Carmen is considering investing $12,000 in Project ABC, which will generate cash flows as follows:
Year 1 -$20,000; Year 2 -$1,000; Year 3 $15,000; Year 4 $27,000; Year 5 $32,000
Using a discount factor of 13%, what is the net present value of this investment?

Answer 73

The net present value of this project is a positive $13,841.41, which means Carmen should invest in the project.

Question 74

Sandra is considering investing in two different projects. Project Fireside requires an initial investment of $50,000, while Project Logic requires an initial investment of $125,000. The table outlines the cash flows for the two projects.
Fireside: Year 1 $5,000; Year 2 $15,000; Year 3 $25,000; Year 4 $30,000
Logic: Year 1 -$5,000; Year 2 $50,000; Year 3 $60,000; Year 4 $65,000
Using a discount rate of 10%, which of the two projects offers a stronger financial case for investment? In addition, using the same cash flow information, calculate the internal rate of return for each of these projects. There are four answers to this question.

Answer 74

Fireside has a net present value of $6,215.42 and Logic has a net present value of $1,251.26. Based on the NPV of each project, Fireside is the better investment. The IRR for the Fireside project is 14.44%, and the IRR for the Logic project is 10.35%. In both cases, the IRR is greater than the cost of capital (10%), which indicates that both projects are economically viable.

Question 75

Bob has a marginal tax rate of 22% and is going to make an investment with an expected rate of return of 8%. Assuming inflation is 2.5%, calculate his a) real rate of return, b) his after-tax rate of return, and c) his real after-tax rate of return. This problem has three answers.

Answer 75

Bob’s real rate of return is 5.37%, his after-tax rate of return of 6.24%, and his real after-tax rate of return is 3.65%.

Question 76

Jim has a marginal tax rate of 40% and is going to make an investment with an expected rate of return of 10%. Assuming inflation is 2%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 76

Jim’s real rate of return is 7.84%, his after-tax rate of return of 6.00%, and his real after-tax rate of return is 3.92%.

Question 77

Mike has a marginal tax rate of 45% and is going to make an investment with an expected rate of return of 9%. Assuming inflation is 1.5%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 77

Mike’s real rate of return is 7.39%, his after-tax rate of return of 4.95%, and his real after-tax rate of return is 3.4%.

Question 78

Don has a marginal tax rate of 35% and is going to make an investment with an expected rate of return of 7.5%. Assuming inflation is 2.5%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 78

Don’s real rate of return is 4.88%, his after-tax rate of return of 4.88%, and his real after-tax rate of return is 2.32%.

Question 79

Rick has a marginal tax rate of 30% and is going to make an investment with an expected rate of return of 8.5%. Assuming inflation is 1.5%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 79

Rick’s real rate of return is 6.90%, his after-tax rate of return of 5.95%, and his real after-tax rate of return is 4.38%.

Question 80

Charlie has a marginal tax rate of 20% and is going to make an investment with an expected rate of return of 11%. Assuming inflation is 1.0%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 80

Charlie’s real rate of return is 9.9%, his after-tax rate of return of 8.80%, and his real after-tax rate of return is 7.72%.

Question 81

Alex has a marginal tax rate of 48% and is going to make an investment with an expected rate of return of 5%. Assuming inflation is 2.0%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 81

Alex’s real rate of return is 2.94%, his after-tax rate of return of 2.60%, and his real after-tax rate of return is 0.59%.

Question 82

Brent has a marginal tax rate of 15% and is going to make an investment with an expected rate of return of 12%. Assuming inflation is 1.5%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 82

Brent’s real rate of return is 10.34%, his after-tax rate of return of 10.20%, and his real after-tax rate of return is 8.57%.

Question 83

Ken has a marginal tax rate of 22% and is going to make an investment with an expected rate of return of 5%. Assuming inflation is 1.0%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 83

Ken’s real rate of return is 3.96%, his after-tax rate of return of 3.90%, and his real after-tax rate of return is 2.87%.

Question 84

Larry has a marginal tax rate of 28% and is going to make an investment with an expected rate of return of 15%. Assuming inflation is 3.0%, calculate his real rate of return, his after-tax rate of return, and his real after-tax rate of return. This problem has three answers.

Answer 84

Larry’s real rate of return is 11.65%, his after-tax rate of return of 10.80%, and his real after-tax rate of return is 7.57%.