# Homework 4

P6. Determine the present values if \$5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations:

5 percent for ten years = PV= 5000/(1+0.05)^10 = 5000/1.6288 = FV = \$3,069.7446

7 percent for seven years = PV= 5000/(1+0.07)^7 = 5000/1.6057 = FV = \$3,113.906

9 percent for four years = PV = 5000/(1+0.09)^4 = 5000/1.4115 = FV = \$3,542.3308

P9. Assume you are planning to invest \$5,000 each year for six years and will earn 10 percent per year. Determine the future value of this annuity if your first \$5,000 is invested at the end of the first year.Used formula;

FVa = PMT {(1+r)^n -1/r}

First year 5000{(1+0.10)^1 -1 /0.10} = 5000{1.10-1/.10} = 5000 (.10/.10) = \$5,000

Second year; 5000{(1+0.10)^2 -1 /0.10} =5000{(1.10)^2 -1 /0.10}= 5000{1.21-1 /0.10}= 5000{.21/.10}= 5000(2.10) = FV= \$10,500

Third year; 5000{(1+0.10)^3 -1 /0.10} = 5000{(1.10)^3 -1 /0.10} = 5000{1.331-1 /0.10}= 5000{.331 /0.10}= 5000{3.31} =FV= \$16,550

Fourth year; 5000{(1+0.10)^4 -1 /0.10} = 5000{(1.10)^4 -1 /0.10} = 5000{1.4641-1/0.10} =5000{.4641 /0.10} = 5000{4.641} = FV = \$23,205

Fifth year; 5000{(1+0.10)^5 -1 /0.10} = 5000{(1.10)^5 -1 /0.10} = 5000{1.6105-1 /0.10} = 5000{(.6105 /0.10} = 5000{6.105} = FV = \$30,525

After six years = 5000{(1+0.10)^6 -1/0.10} = 5000{1.7715-1/.10} = 5000{0.7715/0.10} = 5000(7.715)= FV=38,575.00

P10. Determine the present value now of an investment of \$3,000 made one year from now and an additional \$3,000 made two years from now if the annual discount rate is 4 percent.

Using formula; PV = FV/(1+r)^n

First year; \$3,000/(1+0.04)^1 = 3000/1.04 = FV= \$2,884.61

Second year; \$3,000/(1+0.04)^2 = 3000/1.0816 = FV= \$2,773.66

P11. What is the present value of a loan that calls for the payment of \$500 per year for six years if the discount rate is 10 percent and the first payment will be made one year from now? How would your answer change if the \$500 per year occurred for ten years?

Using formula PV = FV/(1+r)^n

First year; 500/(1+10%)^1 = 500/(1+0.10)^1 =500/1.10 = PV= 454.5454

Second Year; 500/(1+10%)^2 = 500/(1.10)^2 = 500/1.21 = PV = 413.2231

Third year; 500/(1+10%)^3 = 500/(1.10)^3 = 500/1.331 = PV = 375.6574

Fourth Year; 500/(1+10%)^4 = 500/(1.10)^4 = 500/1.4641 = PV = 341.5067

Fifth year; 500/(1+10%)^5 = 500/(1.10)^5 = 500/1.6105 = PV = 310.4625

For six years; 500/(1+10%)^6 =500/(1+0.10)^6 = 500/(1.10)^6 = 500/1.7715 = PV = \$282.24

How would it be for 10 years?

500/(1+10%)^10 = 500/(1.10)^10 =500/2.5937 = PV=192.7748

P12. Determine the annual payment on a \$500,000, 12 percent business loan from a commercial bank that is to be amortized over a five-year period.

A= P{r(1+r)^n/(1+r)^n-1}

P= \$500,000 initial principal loan, A= payment amount per period, r = 12% interest rate per period, n = 5 years (it is an annual payments)

500,000{.12(1+.12)^5/(1+.12)^5-1} = 500,000{.12(1.12)^5/(1.12)^5-1} = 500,000{.12(1.7623)/1.7623-1} = 500,000{.2114/.7623} = 500,000(.2774) = A = \$138,709.1696

P13. Determine the annual payment on a \$15,000 loan that is to be amortized over a four-year period and carries a 10 percent interest rate. Also prepared a loan amortization schedule for this loan.

P= principal loan \$15,000, r=interest rate 10%, n=number of payments (which payments are annual) 4, A=payment amounts per period

15,000{0.10(1+0.10)^4/(1+.10)^4-1} = 15,000{.10(1.10)^4/(1.10)^4-1} = 15,000{.10(1.4641)/1.4641-1} = 15,000{.14641/.4641}= 15,000{.3154}= A= \$4732.06

Basic loan info:

 Loan Amount \$15,000 Annual Interest rate 10% Term of Loan in Years 4 First Payment Date 9/1/2015 Payment Frequency Annually Compound Period Annually Payment Type End of Period

Summary of loan

 Rate per period 10% Number of payments 4 Total money paid \$18,928.24 Total in Interest \$3,928.24 Loan Schedule Every year Principal Vs Interest Loan Balance First Payment 2/1/2018 \$4,732.06 \$3,750 on principal (\$982.06 on interest) \$11,250 in principal loan Second Payment 2/1/2019 \$4,732.06 \$3,750 on principal (\$982.06 on interest) \$7,500 in principal loan Third Payment 2/1/2020 \$4,732.06 \$3,750 on principal (\$982.06 on interest) \$3,750 in principal Fourth Payment 2/1/2021 \$4,732.06 \$3,750 on principal (\$982.06 on interest) \$0.00

P15. Assume a bank loan required an interest payment of \$85 per year and a principal payment of \$1,000 at the end of the loan’s eight-year life.

How much could this loan be sold for to another bank if loans are similar quality carried an 8.5 percent interest rate? That is, what would be the present value of this loan?

1000/8=125 125+85=210 210/.085= \$2470.59

Now, if interest rates on other similar quality loans are 10 percent, what would be the present value of this loan?

210/.1= \$2100.00

What would be the present value of the loan if the interest rate is 8 percent similar-quality loans?

210/.08= \$2625.00