Question

A woman purchases a 10-year par bond with 8% semi-annual coupons. The bond is priced to yield 7.5% converted semi-annually. The coupons are reinvested in a fund paying 7.0% nominal, converted semi-annually. What is her nominal annual yield on this investment, convertible semi-annnually?

Answer 1

Present Value of the bond = [(Coupon Payments_i/(1 + r)ⁱ)] + maturityvalue/(1 + r)ⁿ

= $40/1.0375¹ + $40/1.0375² + ... + $40/1.0375²⁰ + $1000/1.0375²⁰

= $38.55 + $37.16 + ... + $19.16 + $478.89

= $1,034.74

Deposits' FV = P[{(1+r)ⁿ - 1} / r]

= $40[{1.035²⁰ - 1} / 0.035]

= $40[0.9898/0.035] = $40 x 28.28 = $1,131.19

Total Payment at maturity = $1,131.19 + $1,000 = $2,131.19

Investment Yield:

$1,034.74(1 + i)²⁰ = $2,131.19

(1 + i)²⁰ = $2,131.19/$1,034.74

(1 + i) = (2.06)^1/20

1 + i = 1.037

i = 1.037 - 1 = 0.037

so, i = 3.7% per period, or 7.4% per year.