A 25-year, $10,000 strip bond was first issued at 6% compounded semi-annually. Nine years before maturity it was sold on the bond market at a price that would provide the purchaser with a yield rate of 6.8% compounded semi-annually. What was the selling price at that time?
A) $3,430
B) $3,883
C) $5,478
D) $5,874
E) $6,246

Question

Quizplus · Accepted Answer

The selling price of the bond can be calculated using the formula for the present value of a bond, which is the sum of the present value of the principal amount and the present value of the interest payments. However, since this is a strip bond, there are no periodic interest payments, and the bond's value is solely based on the present value of its face value at maturity. Given:- Original issue: 25 years at 6% compounded semi-annually.- Time until maturity when sold: 9 years, meaning it was held for 16 years (25 - 9 = 16).- Yield rate at sale: 6.8% compounded semi-annually.To find the selling price, we calculate the present value of the $10,000 face value due in 9 years at the 6.8% semi-annual yield rate. The formula for the present value $PV = FV / (1 + r)^n$, where $FV$ is the face value, $r$ is the semi-annual yield rate, and $n$ is the total number of compounding periods.- $FV = $10,000$- $r = 6.8\% / 2 = 3.4\% = 0.034$ (since it's compounded semi-annually)- $n = 9 \times 2 = 18$ (since there are 9 years left and it compounds semi-annually)$PV = $10,000 / (1 + 0.034)^{18}$$PV = $10,000 / (1.034)^{18}$$PV = $10,000 / 1.8194$$PV ≈ $5,478$Therefore, the selling price of the bond nine years before maturity, to yield a rate of 6.8% compounded semi-annually, was approximately $5,478.

A 25-Year, $10,000 Strip Bond Was First Issued at 6