Q1 through 10 are worth 4 points each; Q11a, Q11b, Q12, and Q13 are worth 15 points each. Be
sure to solve according to the method that is requested.
1. What is the Rule of 72? To estimate quickly the number of years it takes to double a sum of
capital given an annual interest rate, or to estimate the annual interest rate it takes to double a
sum of money over a given number of years. The rule of 72 is useful for approximating
doubling time in exponential growth.
2. Solve using the Rule of 72: rate = 8%, years = 18, pv = $7,000. Solve for fv.
fv= 28000.
3. Solve, using the Rule of 72 rate = 4%, years = 18, fv=$8,000. Solve for pv.
72. 4% x 18 years = 72, so the future value = $8,000 means the present value = $4,000
4. Solve, using the Rule of 72: rate =6%, pv=$7,000, fv= $56,000. Solve for years.
5. Solve, using the Rule of 72: pv=$10,000; fv=$160,000; years=10. Solve for rate.
Q6-Q9. Use appropriate tvm table in your textbook's appendix to solve Q6-Q9. For each
question, cite the appropriate table that you are using, show the formula, and then plug-in your
numbers to solve. Show all your work.
Q6 pv= $7,200 rate = 7% periods = 15 Solve for fv
Q7 fv=$15,000
rate = 15% periods = 10 Solve for pv
Q8 payment = $6,000 interest rate =8% number of periods = 10 Solve for pva
Q9 payment = $4,000 interest rate =10% number of periods = 20 Find fva
For Q10-Q13, you many use tvm tables, a financial calculator, or excel to solve. Be sure to show
all the steps in your work: factors & formula if you use the tables; keystrokes if you use a
financial calculator; or formulas if you use excel.
Q10. Stressed and penniless after months of day trading, Mr. Baruch decides to invest his savings
into a conservative growth mutual fund. He plans to retire in 30 years and wants to make annual
deposits into his IRA in order to accumulate a sum of $450,000 at the end of the 30 years. Mr.
Baruch expects to earn 10% per year, on average, in his mutual fund. What should be the amount
of Baruch's annual contributions ?
Q11. On the way to Stop&Shop, you buy a lottery ticket and win $100,000. The catch is that the
money will be paid to to you in two installments: $50,000 today, and $50,000 at the end of 5
years from now.
Q11-a: Assuming an interest rate of 8%, what is the present value of your total lottery payments
?
Q11-b: Suppose that you invest the $50,000 winnings that you receive today and earn 8%
annually for the next 5 years. What is the future value of your total lottery payments ?
12. Investor G. Loeb owns a 5-year, $1000 bond with a 5% coupon. If the yield to maturity on
similar bonds is currently 10%, what is Mr. Loeb's bond worth today?
13. A security analyst is forecasting dividends for Boston Electric over the next four years, as
follows: $1 (Y1), $1.50 (Y2); $2.00 (Y3); $2.75 (Y4). In addition, the analyst expects that the
stock could be sold for $62.25 four years from now. If the required return on the stock is 8%,
what is the stock worth today ?
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