Which of the following amounts is closest to the value of a bond that pays $55 semiannually and has an effective semiannual interest rate of 5%? The face value is $1,000 and the bond matures in 3 years. There are exactly six months before the first interest payment.
A) $1,014.
B) $1,055.
C) $888.
D) $1,025.
E) $1,000.

Question

Quizplus · Accepted Answer

The value of the bond can be calculated using the present value of an annuity formula for the semiannual interest payments, plus the present value of the face value of the bond. The formula for the present value of an annuity is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PMT is the payment per period, r is the interest rate per period, and n is the total number of payments. For the face value, the present value formula is $PV = FV / (1 + r)^n$, where FV is the face value.Given:- Semiannual payment (PMT) = $55- Semiannual interest rate (r) = 5% or 0.05- Number of payments (n) = 3 years * 2 = 6- Face value (FV) = $1,000Calculating the present value of the annuity (interest payments):$PV_{annuity} = 55 \times \left(\frac{1 - (1 + 0.05)^{-6}}{0.05}\right)$Calculating the present value of the face value:$PV_{face} = 1000 / (1 + 0.05)^6$Adding both present values gives the total value of the bond, which is closest to $1,025, making option D the correct answer.

Which of the Following Amounts Is Closest to the Value