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 4.5%. 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

Answer 1

Shortfall of money = $74,598

Explanation :

As per the data given in the question,

Par value of bond = $7,472,582

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

FV of Annuity = P [(1 + r)^n- 1 ÷ r]

where,

P = Periodic payment

r = interest rate

n = Time period

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

r = 4.50%

n = 5 years

FV of Annuity = $448,354.92 × [(1 + 4.50%)^5 - 1) ÷ 4.50%]

=$2,452,820

Shortfall at the end of 5 years is

= $10,000,000 - $7,472,582 - $2,452,820

= $74,598