Question

Compute the difference in the future amount of P500 compounded semi-annually at nominal rate of 5% and if it is compounded continuously both for 5 years at the same rate

with solution

Answer 1

Effective rate when compounded semi-annually = (1+5%/2)^2 - 1 = 5.0625%

Effective rate when compounded continuously = exp(5%) - 1 = 5.1271%

FV of P500 when compounded semi-annually = 500*(1+5.0625%)^5 = P640.04

FV of P500 when compounded continuously = 500*(1+5.1271%)^5 = P642.01

Hence, the difference is P1.97