Question

Danielle can purchase a municipal bond with a par value of $5,000 that will mature in three and a half years. The bond pays 8% interest compounded quarterly. If she can buy this bond for $4,800, what rate of return will she earn?

Answer 1

This rate of return is called the "yield to maturity" (YTM) of a bond. It can be explained as the compound rate of return over the life of the bond assuming that all the coupon (interest) payments are reinvested at a rate equal to the YTM of the bond. The formula to calculate YTM is given by:

Here,

C = annual interest payment

M = par value of the bond

P = present value of the bond

n = number of years to maturity

Now,

C = $ 5000 x effective interest rate for quarterly compounding

(In this case, since interest rate is stated annually but compounded quarterly, we will first calculate the effective interest rate for quarterly compounding using the formula -

effective rate = )

= $ 5000 x 0.08243216

= $ 412.1608

M = $ 5000 (given)

P = $ 4800 (given)

n = 3.5 years

therefore, YTM using the formula given above would be -

YTM =

= 0.08738658079 or 8.74%

Danielle will earn 8.74% rate of interest.