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.