Question

A​ zero-coupon bond can be redeemed in 20 years for $ 10 comma 000.$10,000. how much should you be willing to pay for it now if you want a return​ of:

Answer 1

If a zero-coupon bond can be redeemed in 20 years for $10,000:

a.)     If 10% compounded monthly:

 

10,000 = P {1 + (.10 / 12)}^(12)(20) / P {1 + (.10 / 12)}^(12)(20) / P {1 + (.10 / 12)}^(12)(20)

= 7.328073633249730071995931977855 / 7.328073633249730071995931977855 / 7.328073633249730071995931977855

= 0.13646151090276871636035564271905

= 10,000 * 0.13646151090276871636035564271905

= 1364.6151090276871636035564271905

P = $1364.62

You should be willing to pay $1364.62 for it now if you want a return of 10% compounded monthly.

 

b.)    If 10% compounded continuously:

A = Pe^rt

10,000 = Pe^(10)(20) / e^(10)(20) / e^(10)(20)

$1353.35 = P

You should be willing to pay $1353.35 for it now if you want a return of 10% compounded continuously.