Assume a bank loan requires an interest payment of $85 per year and a principal
ID: 2743113 • Letter: A
Question
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.
a. how much 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?
b. Now, if interest rates on other similar quality loans are 10 percent, what would be the present value of this loan?
c. What would be the present value of the loan if the interest rate is 8 percent on similar-quality loans?
PLEASE SHOW DETAIL WORK
Explanation / Answer
A./
PRESENT VALUE OF LOAN - INTEREST RATE 8.5%
= INTEREST * PVIFA 8.5%,8PERIODS + MATURITY * PVIF 8.5%, 8PERIODS
= $85 * 5.6392 + $1000 * 0.5207
= $479.33 + $520.70
= $1000.03 OR $1000 ROUNDED
B./
PRESENT VALUE OF LOAN - INTEREST RATE 10%
= INTEREST * PVIFA 10%,8PERIODS + MATURITY * PVIF 10%, 8PERIODS
= $85 * 5.3349 + $1000 * 0.4665
= $453.45 + $466.50
= $919.95 OR $920 ROUNDED
C./
PRESENT VALUE OF LOAN - INTEREST RATE 8%
= INTEREST * PVIFA 8%,8PERIODS + MATURITY * PVIF 8%, 8PERIODS
= $85 * 5.7466 + $1000 * 0.5403
= $488.46 + $540.30
= $1028.76
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