Question

The bank made a 3-year loan 7% discount rate, with no coupons and a par value of $1,000. If immediately after the loan was made, because of higher inflation expectations, the discount rate increased to 9%. What is the effect of the interest rate change on the value of the loan?

(a) Declines by 1.94%
(b) Increases by 5.4%
(c) Increases by 2.0%
(d) Declines by 5.4%

Answer 1

The increase in the discount rate from 7% to 9% following the issuance of a 3-year maturity loan results in a decline in the value of the loan due to a higher present value discount rate, making option (d) Declines by 5.4% the correct answer.

Step-by-step explanation:

When the discount rate on a loan increases, it affects the present value of the future payments that the borrower needs to make. In the event of a loan being made with a 3-year maturity at a 7% discount rate and then the rate increases to 9%, the value of the loan declines. This is because the present value of the loan's future repayments, now being discounted at a higher interest rate, decreases, similar to how the value of a bond would drop if the interest rates increased post-purchase. Thus, the increase in the discount rate from 7% to 9%, in this scenario, would result in a decline in the value of the loan. Therefore, among the options provided, the correct answer would be (d) Declines by 5.4%.