Question

You manage a pension fund that promises to pay out $10 million to its contributors in five years. You buy $7472582 worth of par-value bonds that make annual coupon payments of 6% and mature in five years. Right after you make the purchase, the interest rate on same-risk bonds decreases to 5.2%. If the rate does not change again and you reinvest the coupon payments that you receive in same-risk bonds, how much will you fall short of the money that you promised? Write your answer as a positive number and round it to the nearest dollar.

Answer 1

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Answer:

At the end of 5 years, the par value of the bonds will be recovered, i.e. $7,472,582.

To determine the future value of annual coupon payments received, we will use the FV of ordinary annuity's formula:

Here, P = 6% of $7,472,582 = $448,354.92

r = Interest rate = 5.20%

n = 5 years

FV of annuity = $448,354.92 * [ {(1+5.20%)^5-1}/5.20% ] = $2,487,361.65

Shortfall at end of 5 years = $10,000,000 - $7,472,582 - $2,487,361.65 = $40,056.8 ~ 40057