Question 1103250
5% interest per year compounding monthly give you more future value than 5% compounding semi-annually.


the reason has to do with the way that the formula for compound interest works.


the formula for compound interest is f = p * (1 + r/c) ^ (n*c)


f is the future value
p is the present value
r is the annual interest rate
n is the number of years.
c is the number of compounding periods per year.


if you invest 1000 for 20 years at 5% per year compounded semi-annually, the formula becomes:


f = 1000 * (1 + .05/2) ^ (20*2).


solve for f to get f = 2685.06


if you invest 1000 for 20 years at 5% per year compounded monthly, the formula becomes:


f = 1000 * (1 + .05/12) ^ (20*12).


solve for f to get f = 2712.64


compounding 12 times a year gives you a higher effective interest rate than compounding 2 times per year.


effective interest rate for compounding 2 times per year is (1 + .05/2) ^ 2 - 1 = .050625 per year.


effective interest rate for compounding 12 times per year is (1 + .05/12) ^ 12 - 1 = .0511618979 per year.