Question

Suppose that today you buy a 9% coupon bond making annual payments for $1,150. The bond has 10 years to maturity. What rate of return do you expect to earn on your investment?

I got answer as 6.88% but could not understand please can someone elaborate

Answer 1

Given 9% coupon rate, So, coupon payment will be 90. Bond price is 1150. Let r be the return we earn on the investment. With 10 years to maturity, we get,

1150= 90/(1+r)+90/(1+r)^2+90/(1+r)^3+......90/(1+r)^9+90/(1+r)^10+1000/(1+r)^10

we can use present value of annuity formula here, which is C*(1-(1+r)^-n)/r, where C is annual payments, r is the rate of return and n is the number of periods. On substituting, we get

1150= (90*(1-(1+r)^-10)/r)+1000/(1+r)^10

On solving the equation, we get r= 6.88%