Question

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:
percent for ten years

percent for seven years

percent for four years

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.

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.

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?

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.

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 prepare a loan amortization schedule for this loan.

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

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

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

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

Answer 1

Answer:

1)

the %s were missing so I looked for a similar question:

we must use the present value formula:

present value = future value / (1 + interest rate)ⁿ

5% ⇒ $5,000 / 1.05¹⁰ = $3,069.57

7% ⇒ $5,000 / 1.07⁷ = $3,113.75

9% ⇒ $5,000 / 1.09⁴ = $3,542.13

2)

we can use the future value of an annuity formula:

future value = annual payment x annuity factor

FV = $5,000 x 7.7156 (FV annuity factor, 10%, 6 years) = $38,578

3)

PV = $3,000/1.04 + $3,000/1.04² = $2,884.62 + $2,773.67 = $5,658.29

4)

present value of an annuity = $500 x 4.3553 (PV annuity factor, 10%, 6 periods) = $2,177.65

present value of an annuity = $500 x 6.1446 (PV annuity factor, 10%, 10 periods) = $3,072.30

5)

annual payment = present value / annuity factor = $500,000 / 3.6048 (PV annuity factor, 12%, 5 years) = $138,703.95

6)

annual payment = present value / annuity factor = $15,000 / 3.1699 (PV annuity factor, 10%, 4 years) = $4,732.01

7)

the value of the loan = PV of the principal + PV of the interest payments

PV of the principal = $1,000 / 1.085⁸ = $520.67

PV of interest payments = $85 x 5.63918 (PV annuity factor, 8.5%, 8 periods) = $479.33

market value of the debt = $1,000

8)

the value of the loan = PV of the principal + PV of the interest payments

PV of the principal = $1,000 / 1.085¹⁰ = $442.29

PV of interest payments = $85 x 5.3349 (PV annuity factor, 10%, 8 periods) = $453.47

market value of the debt = $895.76

9)

the value of the loan = PV of the principal + PV of the interest payments

PV of the principal = $1,000 / 1.08⁸ = $540.27

PV of interest payments = $85 x 5.7466 (PV annuity factor, 8.5%, 8 periods) = $488.46

market value of the debt = $1,028.73