Question

17-1 Consider a 6 percent 10-year bond purchased at face value($1000). Assuming a reinvestment rate of 5 percent, calculate

1. The interest on interest =
2. the total dollar return =
3. the realized compound yield =

Answer 1

Yearly coupon interest = $1,000 6% =$ 60

the same amount will received from the bond for 10 years. Hence the total coupon rate for 10 years = $ 60 10 years= $ 600  

Each years coupon rate is reinvested for an interest of 5%= 0.05.

First years coupon amount of $60 is reinvested for a period of next 9 years then the amount will be

$60 (1 + 0.05)^9 = 93.0796

Reinvestment amount	amount of coupon	Reinvestment Interest
$60 (1 + 0.05)^9 = 93.0796	$60	33.0796
$60 (1 + 0.05)^8= 88.6473	$60	28.6473
$60 (1 + 0.05)^7= 84.4260	$60	24.4260
$60 (1 + 0.05)^6= 80.4057	$60	20.405
$60 (1 + 0.05)^5= 76.5769	$60	16.5769
$60 (1 + 0.05)^4= 72.9303	$60	12.9303
$60 (1 + 0.05)^3= 69.4575	$60	9.4575
$60 (1 + 0.05)^2= 66.15	$60	6.15
$60 (1 + 0.05)^1 = 63.00	$60	3.00

Last years coupon $60 cannot be reinvested

Total Interest on Interest for coupon rate of $60 dollar reinvested @5% interest will fetch = 154.6726 $

Total return = $1000 + $600 +154.67 = $1754.67

Coupon Yield = $ 60   10 years = $ 600

( The problem is attempted on the assumption that the compounding is done only for reinvestment of coupon rates. And the coupon interest for 10 years follows simple interest principle)

If in otherwise the compounding is done for coup interest it will give the answer differently