Chapter 9: Time Value of Money Flashcards
Annuity
A series of consecutive payments or receipts of equal amount.
Ordinary: end
Due: beginning
Compound over additional perioids step
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
How to solve deferred annuity
1 = 1000
2 = 2000
3 = 3000
4-8 = 1,000
8% discount rate
- NPV of annuity (value at yr 3) - then discount 8%, 3 years
- PV of years 1-3 (NPV seperate)
1 = 3992.71 -> 3,169.54
2= 5,022
= total 8,192
A dollar today is worth more than a dollar to be received in the future because
the dollar can be invested today and earn interest.
Time value of money considers ___ will change the value of money?
interest
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?
FV=PV×FVIF(Appendix A: 6%,10 periods)
= $200,000 × 1.791 = $358,200
If you invest $10,000 today at 10% interest, how much will you have in 10 years?
Explanation
FV=PV×FVIF(Appendix A: 10%,10 years)
= $10,000 × 2.594 = $25,940
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?
FV=PV×FVIF(Appendix A: 8%,4 periods)
= $5,000 × 1.360 = $6,800
$6,800 − Initial investment of $5,000 = $1,800
The future value of a $500 investment today at 8% annual interest compounded semiannually for five years is _________
740
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 _________
1,082
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?
$5,637
A home buyer signed a 20-year, 8% mortgage for $72,500. Given the following information, how much should the annual loan payments be?
$7,384
As the time period until receipt increases, the present value
decreases.
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?
($4,134)
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?
8%
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?
above 10%
After 10 years, some shares of stock originally purchased for $500 total were sold for $900 total. What was the yield on the investment?
6%
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?
25,298
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.
$24,294
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?
$20,380
How much must you invest today at 10% interest in order to see your investment grow to $5,000 in 3 years?
$3,755
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?
Between 6% and 8%
