Question

5 years ago, you paid $1065 for a $1,000 par bond that has a 7% coupon with semiannual payments. You are selling it today for $976. You reinvested coupons at the 4% annual rate. What is your total return?

Answer 1

Selling price=   $976  
Purchase price=   1065  
Semiannual Coupon = Face Value*Coupon rate*1/2      
Coupon received =1000*7%/2=   $35  
No of coupons received (n) = 5 years*2 coupon per year=   10  
annual interest rate of reinvestment=   4%  
Semiannual rate(i) =4%/2=   2%  
$10 coupon reinvested each time. So it forms Annuity. future value of Annuity Formula will be applicable to Calculate amount received at time of Sale      
future value of Coupon amount reinvested = P* (((1 +i)^n)-1)/i      
35* (((1 +2%)^10)-1)/2%      
383.240235      
      
Total Return in Dollars = Sale Value- purchase price + Coupon reinvestment future value      
976-1065+383.24      
$294.24      
in % = 294.24/1065=   27.63%  
      
So total Return is    $294.24  
in % it is   27.63%  
      
      
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