Question

A​ zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it​ matures; no interest payments are made. A​ zero-coupon bond can be redeemed in 20 years for $ 10 comma 000. How much should you be willing to pay for it now if you want a return​ of: ​(a) 9​% compounded monthly question mark ​(b) 9​% compounded​ continuously?

Answer 1

Answer:

P = $1664.12 pay with 9​% compounded monthly  

P = 1652.98 pay with  9​% compounded​ continuously

Explanation:

given data

time period = 20 year

amount = $10000

solution

we get here compound interest for 9​% compounded monthly that is express as

FV = $P\times (1+\frac{r}{n})^{nt}$    .................1

here P is principal amount and r is interest rate and n compound in year and FV is future value

$10000 = $P\times (1+\frac{r0.09}{12})^{12\times 20}$  

solve it we get

P = $1664.12 pay with 9​% compounded monthly  

and

for 9​% compounded​ continuously

FV = $P\times e^{rt}$   ............2

$10000 = P\times e^{0.09\times 20}

solve it we get

P = 1652.98 pay with  9​% compounded​ continuously