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A $10{,}000$ par value $10$-year bond with $8\%$ annual coupons is bought at a premium to yield an annual effective rate of $6\%$. Calculate the interest portion of the $7$th coupon.

The solution (image) is the following:

The book value at time $6$ is the present value of future payments: \begin{equation}BV_6=10,000\nu^4+800a_{4\rceil0.06}=7920.94+2772.08=10,693.\end{equation}

The interest portion is $10,693(0.06)=641.58$.

Why is $n$ equal to $4$ in this case? How did they get $4$? Also is it $BV_6$ because the question asks for the interest portion of the $7^{th}$ coupon?

user400188
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musik lover
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1 Answers1

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It's a 10-year bond. To get the interest portion of the 7th coupon, you need to account for the balance present at the start of accrual of that coupon, i.e. at the 6-year point.

There are 4 years from that 6-year point until the maturity of the bond.

gt6989b
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