How to solve Bonds — coupon reinvestment: total accumulated value, realized reinvestment yield, and accumulated coupon interest questions on Exam FM?

Question

A bond with face amount $5,000$, redeemable at $1,000$, pays coupons at $6.54\%$ per period for $n = 7$ periods. Each coupon is reinvested at an annual effective rate of $j = 3.19\%$. Calculate the accumulated interest earned on the reinvested coupons (the reinvestment earnings in excess of the coupons themselves) by time $n$.

Accepted Answer

Formula
$AV=Fr\,s_{\overline n|j}+C$, where $s_{\overline n|j}=((1+j)^n-1)/j$; realized yield satisfies $P(1+y)^n=AV$.

Why this formula applies
Accumulate each coupon from its receipt date to the target date at the reinvestment rate, then add redemption. Coupon interest is the accumulated coupon value minus the coupons themselves.

Substitution and calculation
$s_{\overline{7}|j} = \dfrac{(1+j)^{7}-1}{j} = 7.706674$, so the reinvested coupons accumulate to $Fr\,s_{\overline{7}|} = 327.00\cdot7.706674 = 2,520.0826$. Accumulated coupon interest $= Fr\,s_{\overline{n}|} - nFr = 2,520.0826 - 7\cdot327.00 = 231.0826$.

Answer
The answer is 231.0826, option (B).

How to Solve Bonds — coupon reinvestment: total accumulated value, realized reinvestment yield, and accumulated coupon interest Questions on Exam FM

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