Question

17*A $10,000 mortgage bond with a bond interest rate of 8% per year, payable quarterly, was purchased for $8,800. The bond was kept until it was due, a total of 5 years. What is correct equation (PWr-PWd=0) to calculate the rate of return "i*" made by the purchaser of the bond?

Answer 1

maturity = 5 yrs

Coupon rate = 8%

face value = 10000

Coupon payments = 8% * 10000 = 800

Initial purchase price = 8800

Let rate of return be i%, then PW at rate of return is zero, so

PW = -8800 + 800*(P/A,i%,5) + 10000*(P/F,i%,5) = 0

800*(P/A,i%,5) + 10000*(P/F,i%,5) = 8800

8*(P/A,i%,5) + 100*(P/F,i%,5) = 88

using trail and error method

When i = 10%, value of expression on left side 8*(P/A,i%,5) + 100*(P/F,i%,5) = 92.418

When i = 11%, value of expression on left side 8*(P/A,i%,5) + 100*(P/F,i%,5) = 88.912

When i = 11.5%, value of expression on left side 8*(P/A,i%,5) + 100*(P/F,i%,5) = 87.225

using interpolation

i = 11% + [(88.912-88)/(88.912-87.225)]*(11.5%-11%)

i = 11% + 0.2703

i = 11.27% (Approx)