John takes a 4-year loan that has 48 end-of-the-month payments of K subject to the nominal annual interest rate of 12% compounded monthly. He uses the loan amount to purchase a $1,000 par value 8 year bond, yielding an annual nominal rate of 8% compounded semi-annually, and paying semi-annual coupons at a nominal annual rate of 6%. Find K.
Solution:
Calculating current price of bond:
Current price of bond consist of two cashflows: annual coupon payments and present value of redemption amount.
Annual coupon rate is 6% paid semi annually.
Therefore, semi annual coupon rate is 3%.
semi annual coupon payments = Face value × coupon rate
= 1000 × 3%
= 30.
The bond is redeemed at the face value of $1000.
Yield of bond is 8% compounded semiannually. Therefore, semiannual rate r is 4%.
The bond is redeemed after 8 years. Number of compounding periods n is 8 × 2 = 16
