Question

Consider an annual coupon bond with a face value of $100,5 years to maturity, and a price of $87. The coupon rate on the bond is 3%. If you can reinvest coupons at a rate of 1.5% per annum, then how much money do you have if you hold the bond to maturity? The total proceeds from holding the bond to maturity are $ (Round to the nearest cent.)

Answer 1

Yield to maturity formula c(1 + r)-1 + c(1 + r)-2 + ... + c(1 + r)-Y + B(1 + r)-Y = P. where c = annual coupon payment (in dollars, not a percent) Y = number of years to maturity B = par value P = purchase price

Given

Annual coupon payment = $3

Years to maturity = 5

Par Value = $100

Purchase Price = $87

then substitute these values in the above formula

we get yield to maturity is 6.094 %

If we reinvest the coupon at a rate of 1.5 % per annum

then yield to maturity is 4.46 %

The total proceeds from holding the bond to maturity are $22.30

Answer 2

The return from the bond is known = $100.

You have to find the FV of the reinvested coupons:

(using a financial calculator)

N = 5

PMT = - 3     (100 * 3%)

I/Y = 1.5

CPT FV = 15.46

100 + 15.46 = $115.46