A $63 000 bond bearing interest at 9.1% bond payable semi-annually matures in 20 years. If it is bought to yield 11.1% compounded semi-annually, what is the purchase price of the bond?

Question

Quizplus · Accepted Answer

First we need to calculate the number of semi-annual periods i.e. 20 years x 2 (for semi-annual periods) = 40 semi-annual periods.

Next, we can use the following formula to calculate the present value of the bond:

PV = C x [1 - (1 + r)^-n]/r + FV/(1+r)^n

Where,
PV = Present value of the bond
C = Interest payment every period (semi-annual in this case)
r = Interest rate per period (semi-annual in this case)
n = Total number of periods (semi-annual in this case)
FV = Face value or maturity value of the bond

Now, let's plug in the values:
PV = 63,000 x [1 - (1 + 0.111/2)^-40]/(0.091/2) + 63,000/(1+0.111/2)^40
PV = $52,956.98

Therefore, the purchase price of the bond is $52,956.98.

A $63 000 Bond Bearing Interest at 9