Finance Home Work
1. Rule of 72
It helps in calculating the number of years required for a given amount of money to double at a given interest rate. Calculating how long it takes for the money to double, 72 is divided by the compound rate of return.
2. Solve using the Rule of 72: rate = 8%, years = 18, pv = $7,000. Solve for fv.
Solution
72/8=9
18/9= 2
After nine years= $14000
After 18 years= $28000
2. Solve, using the Rule of 72 rate = 4%, years = 18, fv=$8,000. Solve for pv.
solution:
fv= 8000
72/4=18
Pv*2= 8000
Pv= $4000
4. Solve, using the Rule of 72: rate =6%, pv=$7,000, fv= $56,000. Solve for years.
Solution:
72/6= 12
n- period
When n=1 pv doubles= 7000*2= 14000
When n=2 14000*2= 28,000
When n=3 28,000*2=56000
The number of years= 12 *3= 36 years
5. Solve, using the Rule of 72: pv=$10,000; fv=$160,000; years=10. Solve for rate.
Solution:
10,000*2= 20000
20000*2=40,000
40,000*2=80,000
80,000*2=160,000
n = 4
72/i=4
i= 18%
Q6. pv= $7,200 rate = 7% periods = 15 Solve for fv
Solution:
fv= p v (1+r)n
=7,200(1+0.07)15
fv = 7200*2.759
=$19864.8
Q7 fv=$15,000 rate = 15% periods = 10 Solve for pv
Solution:
Pv= fv/(1+r)n
Pv=15000* 1/(1+r)n
Consider the tvm of present value n=10 and r=15%
=15000*0.247
=$3705
Q8 payment = $6,000 interest rate =8% number of periods = 10 Solve for pva
solution:
PVA= {1-}
= {6000/0.08} *1-0. 463= $40275
Q9. payment = $4,000 interest rate =10% number of periods = 20 Find fva
Solution:
FVA= A*{}
=4000* 57.2741
= $229,096
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?
Solution:
FVA= A*{} (Eugene &Michael,2009).
0.1*450,000=A*{1.130}-1
A=45000/16.449
= $2,736
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 you in two installments: $50,000 today, and $50,000 at the end of 5 years from now.
a). Assuming an interest rate of 8%, what is the present value of your total lottery payments
Solution:
Pv= fv/(1+r)n of the sum to be paid after 5 years; n=5 and r=8%
=50,000* 0.681 = 34,050
Total present value= 50,000+34,050= $84,050
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 ?
solution:
fv= p v (1+r)n
=50,000(1.08)5
=$73466.4
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?
Solution:
Pv= pmt{1-(1+i)-n)/i
Pmt- coupon payment
I – interest rate
n- number of years
Pmt= 5%*1000=50
i=10%
pv=50(1-1.1-5)/0.1
=$189.54
Bond worth= pv+1000=$ 1189.54
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?
Solution:
Bond worth = + +
= + +
= $51.58
References
Eugene, F. B. & Michael, C. E. (2009). Financial Management: Theory and
Practice.USA: cengage learning Inc.
