SOLUTION: Would you have an investment that pays 5% interest compounded semi �annually or the others investment that pays 5% compounded monthly? Explain your answer. (6m)

Question 1103250: Would you have an investment that pays 5% interest compounded semi �annually or the others investment that pays 5% compounded monthly? Explain your answer. (6m)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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