Question

Dorothy purchases a 1000 par value 10-year bond with 9% semiannual coupons for 925. She has found a place to invest her coupons at a nominal rate of 7% convertible semiannually. Calculate her nominal annual yield rate convertible semiannually over the ten-year period .

	A.	8.1%
	B.	9.6%
	C.	10.2%
	D.	9.4%
	E.	9.2%

Answer 1

Hence, the correct answer is the last option i.e. option E.   9.2%

Semi annual coupon payments = 9% / 2 Par value = 4.5% x 1,000 = $ 45

All the coupons are reinvested at the rate of 7% convertible semi annually. Hence, interest rate per period = r = 7% / 2 = 3.5%

Number of periods, n = 2 x 10 = 20

Hence, FV of all the coupons reinvested = 45 / r x [(1 + r)ⁿ - 1] = 45 / 3.5% x [(1 + 3.5%)²⁰ - 1] = $  1,272.59

Receipt of par value at the end of the 10 years = par value = 1,000

Hence, total accumulated value at the end of 10 years =  1,272.59 + 1,000 = $  2,272.59

Invested amount = 925

Let i be the nominal interest convertible semi annually.

Hence, 925 x (1 + i / 2)ⁿ = 2,272.59

Or, 925 x (1 + i / 2)²⁰ = 2,272.59

Hence, i = 2 x [(2,272.59 / 925)^1/20 - 1] = 9.19% = 9.2%

Hence, her nominal annual yield rate convertible semiannually over the ten-year period = i = 9.2%

Hence, the correct answer is the last option i.e. option E.   9.2%