# Reinvested yield

A bond has a par value of \$1,000, a time to maturity of 20 years, a coupon rate of 10 percent with interest paid annually, a current price of \$850, and a yield to maturity (YTM) of 12 percent. If the interest payments are reinvested at 10 percent, the realized compounded yield on this bond is: A) 10.00%. B) 12.0%. C) 12.4%. D) 10.9% I see how you would choose the answer, but how would you calculate the answer?

Choosing the answer is easy. Realized compounded yield should be between 10% and 12% -> D (most likely that’ll all you would have to do on the actual exam). Here is your long solution though: FV of coupon payments = 100*(1+(1+10%)+(1+10%)^2+…+(1+10%)^19)=5,727.5 //can use calculator for that // Face value = 1,000 Final value = Sum = 6,727.5 Initial value = 850 Realized compouned yield = (6,727.5/850)^(1/20)-1=10.8975% = approx = 10.9%

Intuitively this would be a rate between the reinvestment rate (10%) and the YTM (12%). With calculus: 1. annuity N=20, I/Y=10, PV=0, PMT=100, CPT FV=5,727.5 2. at the end of 20 years you also have the face value of 1,000 for a total of 6,727.5, make this your FV N=20, PV=-850, PMT=0, FV=6,727.5, CTP I/Y=10.8975%~10.9%

thanks, nice explanation