Question

Dan purchases a 1000 par value 10-year bond with 9% semiannual couponsfor 925. He is able to reinvest his coupon payments at a nominal rate of 7%convertible semiannually.Calculate his nom

Answer 1

Answer:

9.2%

Explanation:

Missing word "Calculate his nominal annual yield rate convertible semiannually over the ten-year period"

Semi annual coupon payments = 9% / 2 = 4.5%

Par value = 4.5% * 1,000 = $45

interest rate per period = r = 7% / 2 = 3.5%

Number of periods, n = 2 x 10 = 20

FV of all the coupons reinvested = 45 / r * [(1 + r)^n - 1]

FV of all the coupons reinvested = 45 / 3.5% * [(1 + 3.5%)^20 - 1]

FV of all the coupons reinvested = $1,272.59

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

Total accumulated value at the end of 10 years =  $1,272.59 + 1,000

Total accumulated value at the end of 10 years = $2,272.59

Invested amount = $925

i = nominal interest convertible semi annually.

$925 * (1 + i / 2)^n = 2,272.59  

925 * (1 + i / 2)^20 = 2,272.59

i = 2 * [(2,272.59 / 925)^1/20 - 1]

I = 9.19%

I = 9.2%

So, his nominal annual yield rate convertible semiannually over the ten-year period is 9.2%