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qwelly [4]
3 years ago
15

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
Business
1 answer:
sesenic [268]3 years ago
4 0

Answer:

8.00%

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%

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