Time Value of Money
1. A rich uncle has promised to pay you $3,160 at the end of each of the next 25 years. If you
invest this money at 4.9%, how much will you have at the end of the 25 years?
5. Hepsibah Sloop put $10,000 under his mattress 20 years ago. Since then, inflation has averaged
1%. What is the real value of his savings?
9. A 20-year annuity has a present value of $42,419,233. If the interest rate is 15%, what is the
annual cash flow?
10. A Treasury bond pays $1 million at the end of 20 years. What is its present value if the interest
rate is 4%?
11. A project is forecast to produce a safe cash flow of $800,000 a year for 20 years. If the discount
rate is 4%, what is the present value of the project?
12. If you invest $100,000 today, how much will your savings be worth at the end of 9 years if the
interest rate is 10%?
15. An annuity due with 10 annual payments has a present value of 1,244,353. If the interest rate is
15%, what is the annual payment?
18. Investment in a Dustinbourne grinder is expected to produce cash flows over the following
7 years of $7 million, $8 million, $9 million, $10 million, $9 million, $8 million, and $7 million.
What is the present value of the project if the discount rate is 5%?
20. You invest $95,525 for 20 years at 11.7%. Inflation over the same period is 4% a year. What is
the real value of your savings at the end of that period?
22. You invest $1 million for 7 years at 5% and then for a further 7 years at 8%. How much will you
have at the end of this time?
23. The discount factor is .8, and the present value of a cash flow is $2,703. What is the cash flow?
24. A deferred annuity makes four equal payments of $129,987 a year starting at the end of year 8.
If the interest rate is 12%, what is its present value
DOWN
2. The winning lottery ticket promises to make 30 payments of $30,000 a year starting immediately. If the interest rate is 5.8%, what is the present value of these payments?
3. An investment in consol bonds promises to provide an interest payment of $2.5 million a year in
perpetuity. If the interest rate is 3.3%, what is the value of this investment?
4. The discount factor is .9. What is the present value of $63,269?
6. If you pay the bank $50 a year for 10 years, it promises to pay you $100 a year forever starting
in year 11. If the interest rate is 4.2%, what is the value of this proposal to you?
7. The nominal interest rate is 13% and inflation is 4%. If you invest $100,000 today, what will be
the real value of your investment at the end of 20 years?
8. What is the value of a payment of $2,125,000 in year 30 if the interest rate is 3.8%?
13. What is the future value of an investment of $20 million at the end of 11 years if the interest rate
is 9%?
14. Henry Hub will retire in 25 years and expects to spend a further 20 years in retirement (i.e., years
26–45). He lives an extravagant lifestyle and has drawn up a detailed spreadsheet that suggests he
will spend $256,880 a year in real terms in retirement. If the real interest rate is 3%, how much
does Henry need to save each year in real terms until retirement to attain his spending goal?
16. A factory is forecast to produce the following cash flows: year 1, $6,516; year 2, $7,000; year 3,
$11,400; year 4 onward in perpetuity, $12,000. If the cost of capital is 6%, what is the factory’s
present value?
17. What is the future value of $189,956 at the end of 7 years if the interest rate is 11%?
19. Natasha Petrov has savings of $78,780. If she invests the full amount in a bank at an interest rate
of 4%, how much will she have after 4 years?
21. You plan to save $1,000 a year in each of years 1 through 5. If the interest rate is 8%, how much
will you have saved by the end of year 5?
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