Chapter 5 - Time Value of Money Flashcards
List the 2 ways to calculate interest
- Simple interest
- Compount interest
What is calculated as a percentage of the principal?
Simple interest
What is the formula to find simple interest?
Money invested + (Years x Interest on Investment)
Solve the problem:
If you decide to invest $1,000 in a money market account with a simple interest rate of 10%, how much simple interest will you earn after three years?
1,000 + (3 ( 1,000 x 10%)) = 1,300
What is Compound interest?
Interest on Interest
What is the formula to find the compound interest of the second year?
Year 1 ending balance + interest on interest
Solve the problem:
If you invest $1,000 at an interest rate of 10% compounding for 3 years, what will year 3’s ending balance be?
Year 1: 1,000 + (1,000 x 10%) = 1,100
Year 2: 1,100 + (1,100 x 10%) = 1,210
Year 3: 1,210 + (1,210 x 10%) = 1,331
Ending Balance after 3 years = $1,331
Which type of interest will grow your money more over time?
Compound interest
What is it called when you find the future value of a cash flow or series of cash flows?
Compounding
Which calculator buttons do you use to find the future value?
N, I, PV
What is the future value of an initial $100 after 10 years, if interest = 10%?
N = 10, I = 10%, PV = $100
FV = $259.37
What is it called when you find the present value of a cash flow or series of cash flows?
Discounting
What shows the value of cash flows in terms of today’s purchasing power?
Present Value
Solve the problem:
What is the present value of $1,000 due in 3 years, if interest = 12%?
N = 3, I = 12%, FV = $1,000
PV = $711.78
What is a series of payments made at equal intervals?
An annuity
Which calculator buttons do you use to find an annuity?
N, I, PMT
When are Ordinarity Annuity payments due?
At the end of the period
When are Annuity Due payments due?
At the beginning of the period
Solve the problem:
What is the future value of a 3-year ordinary annuity with annual investment of $200, evaluated at a 10% interest rate?
N = 3, I = 10%, PMT = 200
FV = $662.00
Does an ordinary annuity or a annuity due make more money?
Annuity due because you are making more interest
Which calculator buttons do you use to find compound interest?
N, I, PMT
Solve the problem:
A 20-year-old student saves $5 a day for her retirement. At the end of the year, she invests the accumulated savings ($5 x 365 = $1,825) in a brokerage account with an expected annual return of 12%. How much money will she have when she is 65 years old?
N = 45, I = 12%, PMT = $1,825
FV = $2,478,769.81
Solve the problem:
Suppose you are buying your first condo for $180,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 20-year, monthly payment, amortized mortgage at a 5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?
N = 240 (20 x 12), I = .4167 (5%/12), PV = 165,000 (180,000 – 15,000)
PMT = $1,088.93
Solve the problem:
Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $6,500 per month for 30 years, beginning a year from today. The going rate on such annuities is 8%. How much would it cost her to buy such an annuity today?
N = 360 (30 x 12), I = .67 (8%/12), PMT = 6,500
PV = $885,842.71
Solve the problem:
You are considering buying a new car. The sticker price is $35,000, and you have $2,000 to put toward a down payment (your loan amount = $33,000). If you can negotiate a nominal annual interest rate of 1.99% and you wish to pay for the car over a 5-year period, what are your monthly car payments?
N = 60 (5 x 12), I = .1658 (1.99%/12), PMT = 33,000 (35,000 – 2,000)
PV = $578.27
What is an annual rate that ignores compounding effects?
A nominal rate
What is the amount of interest charged each period?
The periodic rate
Will the future value of a lump sum be larger or smaller if compounded more often?
Larger
What is the annual rate of interest actually being earned?
The Effective annual rate
List the 4 steps to find the loan amortization
- Calculate PMT
- Find the Interest Paid in Year 1
- Find the Principal Repaid in Year 1
- Find the Ending Balance after Year 1
Which calculator buttons do you use to find the annual equal payment?
N, I, PV
What is the formula to find the interest paid in year 1?
Beginning balance x interest rate
What is the formula to find the principle repaid in year 1?
PMT - Interest paid
What is the formula to find the loam amortization’s ending balance?
Beginning balance - Principle repaid
True or False:
Interest paid declines with each payment as the balance declines
True
How do you find the future value of an uneven cash flow?
You caluclate the future value of each year and then add them all up
True or False:
Starting to invest early for retirement increases the benefits of compound interest
True
True or False:
A time line is not meaningful unless all cash flows occur annually
False
True or False:
If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series
True
True or False:
Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value
True
True or False:
If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate
False
True or False:
The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date
True
True or False:
The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant
True
True or False:
The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant
False
True or False:
When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage declines in the loan’s later years
False
Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
c. The cash flows for an annuity due must all occur at the ends of the periods.
d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.
Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
c. The cash flows for an annuity due must all occur at the beginning of the periods.
d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
c. The cash flows for an annuity due must all occur at the beginning of the periods.
Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?
a. The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
b. The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
d. The periodic rate of interest is 3% and the effective rate of interest is 6%.
e. The periodic rate of interest is 6% and the effective rate of interest is also 6%.
c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.
a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
Which of the following investments would have the lowest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.
a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?
a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
c. A bank loan’s nominal interest rate will always be equal to or less than its effective annual rate.
d. If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.
e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.
c. A bank loan’s nominal interest rate will always be equal to or less than its effective annual rate.
Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?
a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
c. A bank loan’s nominal interest rate will always be equal to or greater than its effective annual rate.
d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.
e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.
d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.
You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?
a. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.
e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.
Which of the following bank accounts has the highest effective annual return?
a. An account that pays 8% nominal interest with monthly compounding.
b. An account that pays 8% nominal interest with annual compounding.
c. An account that pays 7% nominal interest with daily (365-day) compounding.
d. An account that pays 7% nominal interest with monthly compounding.
e. An account that pays 8% nominal interest with daily (365-day) compounding.
e. An account that pays 8% nominal interest with daily (365-day) compounding.
You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?
a. Bank 1; 6.1% with annual compounding.
b. Bank 2; 6.0% with monthly compounding.
c. Bank 3; 6.0% with annual compounding.
d. Bank 4; 6.0% with quarterly compounding.
e. Bank 5; 6.0% with daily (365-day) compounding.
e. Bank 5; 6.0% with daily (365-day) compounding.
You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?
a. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.
b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
d. The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD.
e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
a. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.
