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)
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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.
