Module 3 - Quiz

Question 1

The real rate of return is?

1) The rate earned on Treasury bills
2) The rate earned on Treasury bonds
3) The rate of inflation
4) The rate earned minus the inflation rate

Answer 1

4) The rate earned minus the inflation rate

The real rate of return subtracts inflation from the rate earned. (This is not the Inflation Adjusted Interest Rate [IAIR], used to solve the PVAD problems.)

Question 2

What effect does an assumption regarding the rate of return have on achieving a goal?

1) An assumption of a high rate of return may result in fewer dollars being invested to achieve a particular goal
2) An assumption of a high rate of return will allow greater flexibility in achieving a particular goal
3) An assumption of a low rate of return may result in fewer years being needed to achieve a particular goal
4) An assumption of a low rate of return will make it possible to achieve a particular goal

Answer 2

1) An assumption of a high rate of return may result in fewer dollars being invested to achieve a particular goal
- May indeed result in fewer dollars being invested to achieve a particular goal because the high return means that fewer dollars will need to be invested.
2) Could very well mean it is less likely that a goal will be achieved since that return might not be realized; flexibility is not the issue.
3) May result in more years being needed to achieve a particular goal.
4) Might make it possible for a particular goal to be achieved, but it gives no assurance that the goal will be achieved.

Question 3

Which one of the following statements is correct, all of the other relevant variables being equal?

1) As the number of compounding periods within a set period of time (such as five years) increases, the future value of an annuity due decreases
2) The future value of an annuity due will be greater than the future value of an ordinary annuity
3) The lesser the compound rate, the larger the future value
4) The present value of an ordinary annuity will be greater than the present value of an annuity due

Answer 3

2) The future value of an annuity due will be greater than the future value of an ordinary annuity
- The future value of an annuity due will be greater than the future value of an ordinary annuity because the money is invested earlier with an annuity due (at the beginning of the period rather than at the end of the period).
1) The future value of an annuity due increases because the effective interest rate is higher. For example, a stated rate of 10% is 10% compounded annually, but it is 10.25% compounded semiannually. The higher the effective interest rate is, the higher the future value is. This means that less money must be invested initially.
3) The smaller the compound rate, the smaller the future value.
4) The present value of an ordinary annuity will be less than the present value of an annuity due since the first payment in an annuity due is not discounted.

Question 4

Steve Williams invested $10,000 in a growth mutual fund five years ago. He earned an average annual return of 9.5% on the fund during that period. How much is his fund worth now?

1) $14,377
2) $15,742
3) $15,905
4) $16,105

Answer 4

END mode
#CP - 1x/yr (not specified)
CLEAR ALL
Solving for FV = $15,742

PV - (10,000)
n - 5
i - 9.5
FV

Question 5

Mary Jones wants to accumulate $100,000 in 12 years. She believes she can earn 7%, compounded annually, on her money. How much does she need to invest today to achieve her goal?

1) $39,711
2) $43,796
3) $44,401
4) $47,509

Answer 5

END mode
#CP - 1x/yr
CLEAR ALL
Solving for PV = $44,401.20

FV - 100,000
n - 12
i - 7
PV

Question 6

George Foster invested $5,000 in a mutual fund 15 years ago. It is now worth $25,250. What average annual rate of return did George earn on this investment?

1) 10.05%
2) 11.10%
3) 11.40%
4) 12.26%

Answer 6

END mode
#CP - 1x/yr
CLEAR ALL
Solving for I = 11.40%

PV - (5,000)
n - 15
FV - 25,250
i

Question 7

Tammy Hill wants to buy a car for $20,000, and finance it with a five-year loan at 6%. What would her monthly payments be?

1) $372.08
2) $386.66
3) $399.07
4) $417.94

Answer 7

END mode
#CP - 12x/yr
CLEAR ALL
Solving for PMT = $386.65

PV - (20,000)
n - 5
i - 6
PMT

Question 8

John Riley plans to invest $2,000 at the beginning of each of the next 18 years. If he can earn 10%, compounded annually, on his investment, how much will he have accumulated at the end of this time period?

1) $91,198
2) $100,318
3) $112,550
4) $126,406

Answer 8

BEG mode
#CP - 1x/yr
CLEAR ALL
Solving for FV = 100,318.18

PMT - (2,000)
n - 18
i - 10
FV

Question 9

Kim Nelson plans to invest $5,000 in a variable annuity at the end of each of the next 25 years. She believes she can earn an average annual return of 12% over this period of time. How much will she have accumulated at the end of 25 years?

1) $572,067
2) $590,776
3) $666,669
4) $746,670

Answer 9

END mode
#CP - 1x/yr
CLEAR ALL
Solving for FV = $666,669.35

PMT - (5,000)
n - 25
i - 12
FV

Question 10

Dave Peters is taking out a 30-year mortgage loan of $200,000 at 6%. Payments are due at the end of each month. How much is Dave’s monthly principal and interest mortgage payment?

1) $1,142.28
2) $1,193.14
3) $1,199.10
4) $1,210.82

Answer 10

END mode
#CP - 12x/yr
CLEAR ALL
Solving for PMT = 1,199.10

PV - (200,000)
n - 30
i - 6
PMT

Question 11

Ann Timmerman plans to invest $30,000 in a savings account that earns interest at 3%, compounded quarterly. At the end of seven years, how much will the account be worth?

1) $35,892
2) $36,896
3) $36,953
4) $36,981

Answer 11

END mode
#CP - 4x/yr
CLEAR ALL
Solving for FV = 36,981.35

PV - (30,000)
n - 7
i - 3
FV

Question 12

Assume an annuity will make payments of $500 at the beginning of each month for the next 20 years, starting today. Using a discount rate of 6%, what is the present value of this annuity?

1) $68,820
2) $69,790
3) $70,139
4) $72,949

Answer 12

BEG mode
#CP - 12x/yr
CLEAR ALL
Solving for PV = 70,139.34

PMT - 500
n - 20
i - 6
PV

Question 13

Jack Taylor invested $100,000, and after one year, the account was worth $107,000. Assuming monthly compounding, approximately what rate of return did he earn?

1) 6.78%
2) 6.82%
3) 6.88%
4) 7%

Answer 13

END mode
#CP - 12x/yr
CLEAR ALL
Solving for I = 6.78%

PV - (100,000)
n - 1
FV - 107,000
i

Question 14

Sue Gregory will receive semiannual payments of $4,000 at the end of each period for the next 10 years. Her first payment will be received six months from today, and her opportunity cost is 8%. What is the present value of these payments?

1) $53,681
2) $54,361
3) $56,536
4) $57,975

Answer 14

END mode
#CP - 2x/yr
CLEAR ALL
Solving for PV = 54,361.31

PMT - 4,000
n - 10
i - 8
PV

Question 15

Wayne Kelly wants to know how long it would take his $10,000 nest egg to grow to $15,000, assuming annual compounding with a 5.5% return. Your answer would be

1) 7.33
2) 7.57
3) 7.69
4) 7.93

Answer 15

END mode
#CP - 1x/yr
CLEAR ALL
Solving for N = 7.57

PV - (10,000)
i - 5.5
FV - 15,000
n

Question 16

How does an assumption on the future rate of inflation impact the achievement of a specific goal?

1) A rate of inflation assumption that is too low may mean that more years will be needed to achieve the goal
2) A rate of inflation assumption that is high may allow greater investment flexibility in achieving the goal
3) A rate of inflation assumption that is high may mean that fewer dollars need to be allocated toward the goal

Answer 16

1) A rate of inflation assumption that is too low may mean that more years will be needed to achieve the goal
- If the rate of inflation is underestimated, it will take more years to achieve a goal since inflation will likely increase the cost of the goal.
2) A rate of inflation assumption that is high may restrict the investment flexibility in achieving that goal. For example, with high inflation, fixed-income securities fall in price, so they would not be considered an appropriate investment in such an environment.
3) A rate of inflation assumption that is high may mean that more dollars need to be allocated toward the goal since the cost of the goal can increase with inflation.

Question 17

Ken Higgins invested $2,000 in an IRA at the beginning of each year for 24 years. If Ken earned interest at a rate of 10% on his account, how much did he accumulate at the end of this time period?

1) $176,995
2) $194,694
3) $216,364

Answer 17

BEG mode
#CP - 1x/yr
CLEAR ALL
Solving for FV = 194,694.12

PMT - (2,000)
n - 24
i - 10
FV

Question 18

Fritz is interested in a $175,000, 30-year mortgage with a 5% fixed interest rate. He has asked you to determine how much his level principal and interest payments would be each month. You would advise him that his payments would be

1) $939.44
2) $825.10
3) $1,061.19

Answer 18

END mode
#CP - 12x/yr
CLEAR ALL
Solving for PMT = 939.44

PV - (175,000)
n - 30
i - 5
PMT

Question 19

How much would a person need to invest at the end of each year in order to accumulate $100,000 in 15 years, assuming the investment could earn an annualized rate of 9%?

1) $3,124
2) $3,406
3) $3,682

Answer 19

END mode
#CP - 1x/yr
CLEAR ALL
Solving for PMT = 3,405.89

FV - 100,000
n - 15
i - 9
PMT

Question 20

When setting goals, it is generally better to

1) assume a higher rate of return rather than a lower rate of return
2) be conservative and assume a 0% return
3) assume a lower rate of return rather than a higher rate of return

Answer 20

3) assume a lower rate of return rather than a higher rate of return
- It is generally better to assume a lower rate of return, and thus need to save more to reach a particular goal. If the return assumption is too high, and then not achieved, the goal will not be met.
1) Assuming a rate of return that is too high increases the chance that a goal won’t be achieved because it could cause too little money to be invested toward that goal.
2) Some sort of return should be earned, and assumed. Just as assuming too high of a return is unrealistic, assuming no return at all is also unrealistic.

Question 21

Which of the following calculations should be done in the “begin” mode?

1) auto loan
2) home mortgage
3) college payments

Answer 21

3) college payments
- Payments for college are due at the beginning of each session, not end, and any calculations involving college payments should be done in the begin mode. This is also the case for payments being made in retirement. Any payments will be made at the beginning of each year to pay for that year of retirement expenses.

Question 22

Which of the following statements about annuities is correct?

1) An ordinary annuity is a stream of payments or receipts made at the end of each period
2) Interest earned on interest is called discounting
3) A home mortgage is an example of an annuity due

Answer 22

1) An ordinary annuity is a stream of payments or receipts made at the end of each period

Question 23

T / F - All else being equal, contributing to an IRA as an annuity due rather than an ordinary annuity will result in a higher account balance in the future.

Answer 23

True - An annuity due would mean that contributions are being made at the beginning of each period, not the end. This gives the contributions more time to earn interest, which will result in a future account balance that is higher.

Question 24

T / F - The future value of an ordinary annuity will be greater than the future value of an annuity due if the interest rates and the time periods of the two annuities are the same.

Answer 24

False - If the interest rates and the time periods are the same, the future value of an ordinary annuity will be less than, not greater than, the future value of an annuity due because the payments or receipts for an ordinary annuity are received later, (at the end of each period) rather than at the beginning of the period.

Question 25

T / F - All else being equal, it is less advantageous to make debt payments as an ordinary annuity rather than an annuity due.

Answer 25

False - All else being equal, it is more advantageous to make debt payments at the end of each period (ordinary annuity) rather than at the beginning of each period (annuity due).

Question 26

James has just won the lottery, and has the choice of either taking a lump sum of $500,000 or receiving a payment of $62,000 at the beginning of each year for the next 10 years. If James believes the opportunity cost is 6%, what should James do?

1) The present value of the annuity is greater than $500,000, so James should take the annuity
2) The $500,000 lump sum is greater than the present value of the annuity, so James should take the lump sum
3) There is no way to determine which option James should choose.

Answer 26

1) The present value of the annuity is greater than $500,000, so James should take the annuity
- Calculate PV of annuity payments compared to lump sum of $500,000

PMT - 62,000
n - 10
i - 6
PV = 483,704.92

The lump sum of $500,000 is greater than the present value of the $62,000 payments.

Question 27

If a future value is $145,000, the annual discount rate is 8%, and the time period is 23 years, then the present value is

1) $24,696
2) $25,898
3) $26,885

Answer 27

END mode
#CP - 1x/yr
CLEAR ALL
Solving for PV = 24,695.72

FV - 145,000
n - 23
i - 8
PV

Question 28

With amortization over time, the amount of each payment being applied to principal is

1) decreasing
2) increasing
3) staying the same

Answer 28

2) increasing
- With each payment the amount being applied to principal is increasing, and the amount being applied to interest is decreasing.

Question 29

Robert has $5000 invested in a mutual fund, and plans on adding $500 at the end of every quarter for the next five years. If he makes all of his quarterly contributions and earns a 7.5% return, what will his investment in the fund be worth in five years?

1) $18,665
2) $19,002
3) $19,248

Answer 29

END mode
#CP - 4x/yr
CLEAR ALL
Solving for FV = 19,248.35

PV - (5,000)
PMT - (500)
n - 5
i - 7.5
FV

Question 30

The present value of $1,000 ordinary annuity payments that are made once a year for nine years and discounted at an annual rate of 6% is

1) $6,802
2) $7,210
3) $7,555

Answer 30

END mode
#CP - 1x/yr
CLEAR ALL
Solving for PV = 6,801.69

PMT - 1,000
n - 9
i - 6
PV

Question 31

Regina wants to accumulate $20,000 in three years to start her own business. She wants to be conservative and only count on earning a 1.5% return. What amount would Regina have to set aside monthly in order to reach her goal?

1) $522.45
2) $533.50
3) $543.50

Answer 31

END mode
#CP - 12x/yr
CLEAR ALL
Solving for PMT = 543.50

FV - 20,000
n - 3
i - 1.5
PMT

Question 32

Zack inherited XYZ stock from his dad when it was worth $12,324. He has held onto XYZ and seven years later it is now worth $33,645. What annual rate of return has Zack earned on his XYZ stock?

1) 15.43%
2) 16.06%
3) 16.85%

Answer 32

END mode
#CP - 1x/yr
CLEAR ALL
Solving for I = 15.43

PV - (12,324)
n - 7
FV - 33,645
i