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

P = $1664.12 pay with 9​% compounded monthly

P = 1652.98 pay with 9​% compounded​ continuously

Step-by-step 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* (1+(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* (1+(r0.09)/(12))^(12* 20)`

solve it we get

P = $1664.12 pay with 9​% compounded monthly

and

for 9​% compounded​ continuously

FV =
`P* e^(rt)` ............2

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

solve it we get

P = 1652.98 pay with 9​% compounded​ continuously