How to solve Bonds — book value, interest earned, and amortization of premium/discount questions on Exam FM?

Question

A bond with face amount $5,000$, redeemable at par, pays $7.93\%$ coupons per period for $n = 10$ periods and yields $3.47\%$ per period. Calculate the write-up or write-down in the $3$th period.

Accepted Answer

Formula
Immediately after coupon $t$, $B_t=Fr\,a_{\overline{n-t}|i}+Cv^{n-t}$, and the recursion is $B_{t+1}=B_t(1+i)-Fr$.

Why this formula applies
At a coupon date, book value equals the present value of remaining cash flows at the yield rate. The recursion earns yield interest, pays the coupon, and leaves the next book value.

Substitution and calculation
With $v = 1/(1+i)$, the prospective book value uses the remaining $n-t$ coupons. $B_{2} = 6534.8132$; the write-down (premium) is $|Fr - i B_{2}| = |396.5000 - 226.7580| = 169.7420$. Requested value: $169.7420$.

Answer
The answer is 169.7420, option (A).

How to Solve Bonds — book value, interest earned, and amortization of premium/discount Questions on Exam FM

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