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1. What is the Rule of 72 ? 2. Solve using the Rule of 72: rate = 8%, years = 18

ID: 2698810 • Letter: 1

Question

1. What is the Rule of 72 ?

2. Solve using the Rule of 72: rate = 8%, years = 18, pv =

$7,000. Solve for fv.

3.Solve, using the Rule of 72rate = 4%, years = 18,

fv=$8,000. Solve for pv.

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 in30 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. InvestorG. Loebowns 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

?


Explanation / Answer

1)
'Rule Of 72'

A rule stating that in order to find the number of years required to double your money at a given interest rate, you divide the compound return into 72. The result is the approximate number of years that it will take for your investment to double.

2)
As per Rule 72, the no. times the investment doubles = 8*18/72 = 2
P.V. = $7000
Thus, F.V. = 7000*22 = $28000.

3)
As per Rule 72, the no. times the investment doubles = 4*18/72 = 1
F.V. = $8000
Thus, P.V. = 8000*2-1 = $4000

4)
P.V.= $7000
F.V. = $56000
The no. time investment doubles:
7000*2x=56000
x = 3
As per Rule 72, the no. times the investment doubles
or, 8*Time/72 = 3
or, Time = 27 years.

5)
P.V.= $10000
F.V. = $160000
The no. time investment doubles:
10000*2x=160000
x = 4
As per Rule 72, the no. times the investment doubles
or, 10*Rate/72 = 4
or, Rate = 28.8%

6)
F.V. = 7200*(1+0.07)15 = $19865

7)
15000 = P.V.*(1 + 0.15)10
or, P.V. = $3708

8)
P.V.A = 6000{(1+0.08)-1 + (1+0.08)-2 + %u2026 + (1+0.08)-10}
= $40260

9)
F.V.A = 4000{(1+0.1)1 + (1+0.1)2 + %u2026 + (1+0.1)20}
= $88957

10)
Thus, the F.V.A. is $450000 at the end of 30 years invested at 10%.
Let the annuity be %u2018x%u2019
450000 = x*{(1+0.1)1 + (1+0.1)2 + %u2026 + (1+0.1)30}
x = $12809

11a)
P.V. = 50000*1.08-0 + 50000*1.08-5
= $84029.

11b)
F.V.A. = 50000 (1+0.08)5 + 50000 = $123466

12)
Price of Bond = 0.05*1000{(1+0.1)-1 + (1+0.1)-2 + %u2026 + (1+0.1)-5} + 1000(1+0.1)-5
= $810.46

13)
Price = 1*(1.08)-1 + 1.5*(1.08)-2 + 2*(1.08)-3 + 2.75*(1.08)-4 + 62.25*(1.08)-4
= $51.58