Chapter 9: Time Value of Money

Question 1

Annuity

Answer 1

A series of consecutive payments or receipts of equal amount.

Ordinary: end
Due: beginning

Question 2

Compound over additional perioids step

Answer 2

In such cases, adjust the normal formula.
n = No. of years × No. of compounding periods during year
i = Quoted annual interest rate / No. of compounding periods during year

Question 3

How to solve deferred annuity

1 = 1000
2 = 2000
3 = 3000
4-8 = 1,000

8% discount rate

Answer 3

1. NPV of annuity (value at yr 3) - then discount 8%, 3 years
2. PV of years 1-3 (NPV seperate)

1 = 3992.71 -> 3,169.54
2= 5,022

= total 8,192

Question 4

A dollar today is worth more than a dollar to be received in the future because

Answer 4

the dollar can be invested today and earn interest.

Question 5

Time value of money considers ___ will change the value of money?

Answer 5

interest

Question 6

You will deposit $200,000 today. It will grow for five years at 12% interest but compounded semi-annually. What will your investment grow to?

Answer 6

FV=PV×FVIF(Appendix A: 6%,10 periods)

= $200,000 × 1.791 = $358,200

Question 7

If you invest $10,000 today at 10% interest, how much will you have in 10 years?

Answer 7

Explanation
FV=PV×FVIF(Appendix A: 10%,10 years)

= $10,000 × 2.594 = $25,940

Question 8

Isaac invests $5,000 in a money market account at his local bank. He receives annual interest of 8% compounded for four years. How much total return will his investment earn during this time period?

Answer 8

FV=PV×FVIF(Appendix A: 8%,4 periods)
= $5,000 × 1.360 = $6,800

$6,800 − Initial investment of $5,000 = $1,800

Question 9

The future value of a $500 investment today at 8% annual interest compounded semiannually for five years is _________

Answer 9

740

Question 10

You will deposit $2,000 today. It will grow for five years at 12% interest but compounded semi-annually. You will then withdraw the funds annually over the next four years at the end of each year, with an annual interest rate of 8%. Your annual withdrawal will be approximately _________

Answer 10

1,082

Question 11

Ethan is creating a college investment fund for his daughter. He will put in $1,000 per year for the next 5 years starting one year from now and expects to earn a 6% annual rate of return. How much money will his daughter have when she starts college?

Answer 11

$5,637

Question 12

A home buyer signed a 20-year, 8% mortgage for $72,500. Given the following information, how much should the annual loan payments be?

Answer 12

$7,384

Question 13

As the time period until receipt increases, the present value

Answer 13

decreases.

Question 14

Mailee will pay out $6,000 at the end of year two and $8,000 at the end of year three. Then Mailee will receive $10,000 at the end of year four. With an interest rate of 10%, what is the net value of the payments versus receipts in today’s dollars?

Answer 14

($4,134)

Question 15

Sureka has just invested $10,000 for her daughter (age 7). The money will be used for her daughter’s education 10 years from now. She calculates that she will need $21,598 for her daughter’s education by the time she goes to school. What rate of return will Sureka need to achieve this goal?

Answer 15

8%

Question 16

Luca has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?

Answer 16

above 10%

Question 17

After 10 years, some shares of stock originally purchased for $500 total were sold for $900 total. What was the yield on the investment?

Answer 17

6%

Question 18

Ezra would like to save $2,000,000 by the time he retires in 30 years. If he believes that he can achieve a 6% rate of return, how much does he need to deposit each year, starting one year from now, to achieve his goal?

Answer 18

25,298

Question 19

Ambrin Corporation expects to receive $2,000 at the end of each year for 10 years. Then the corporation expects to receive $3,500 per year for the following 10 years, at the end of each year. What is the approximate present value of this 20-year cash flow? Use an 8% discount rate.

Answer 19

$24,294

Question 20

Minka borrowed $150,000 to buy a house. Her loan cost was 6% and she promised to repay the loan in 10 equal annual payments. What are Minka’s annual payment amounts?

Answer 20

$20,380

Question 21

How much must you invest today at 10% interest in order to see your investment grow to $5,000 in 3 years?

Answer 21

$3,755

Question 22

Kenya has $210,000 and wants to retire. What approximate return must her money earn so she may receive annual benefits of $30,000 for the next 10 years?

Answer 22

Between 6% and 8%