Question

an n-year bond with par value $1,000 has annual coupons of $82. At a price of $891.62, the yield to the purchaser is 10% compounded semi-annually, calculate n

Answer 1

Par Value = $1,000
Current Price = $891.62
Annual Coupon = $82

Annual YTM = 10.00%
Semiannual YTM = 5.00%

Effective Annual Rate = (1 + Semiannual YTM)^2 - 1
Effective Annual Rate = (1 + 0.05)^2 - 1
Effective Annual Rate = 1.1025 - 1
Effective Annual Rate = 0.1025 or 10.25%

Time to Maturity = n years

$891.62 = $82 * PVIFA(10.25%, n) + $1,000 * PVIF(10.25%, n)

Using financial calculator:
I = 10.25%
PV = -891.62
PMT = 82
FV = 1000

N = 8

Time to Maturity = 8 years