213,940 views
4 votes
4 votes
Doris purchased a zero coupon bond 5 years ago for $675.68. If the bond matures today and the face value is $1,000, what is the average annual compound rate of return (calculated semiannually) that she realized on her investment

User Asma Rahim Ali Jafri
by
2.7k points

1 Answer

5 votes
5 votes

Answer:

8.00%

Step-by-step explanation:

The price of a zero-coupon bond is the present value of its face value since no coupon payments exist, hence, we can determine the semiannual rate of return using the formula below:

PV=FV/(1+r)^n

PV= $675.68

FV=$1000

r=semiannual rate of return=unknown

n=number of semiannual periods in 5 years=5*2=10

$675.68=$1000/(1+r)^10

$675.68*(1+r)^10=$1000

(1+r)^10=$1000/$675.68

$1000/$675.68 can be rewritten as ($1000/$675.68)^1

(1+r)^10=($1000/$675.68)^1

divide indexes on both sides by 2

1+r=($1000/$675.68)^(1/10)

r=($1000/$675.68)^(1/10)-1

r=4.00%(semiannual rate of return)

the annual rate of return(compounded semiannually)=4.00%*2=8.00%

User Brent Parker
by
3.2k points