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Sat 22 Dec, 2012 07:21 pm
Can somebody help me write a formula in which compound interest is expressed but in which a fee is taken off of the principal before each investment period.
Here is the general formula for compund interest.
M=PV*(1+R)^N
PV is the present value (or the principal).
R is the interest rate.
N is the number of investment periods.
The formula I am trying to write, would also involve the variable F=fee.
For example, I have $100, am charged $10 and then I earn my first 25% interest upon that $90. From $112.50, I am then charged another $10 fee, which gives me $102.50, and then I earn another 25% interest. I finish with about $128.13. In this case, PV=$100, R=25%, N=2, F=$10, and M=$128.13.
I would like to have a formula to allow me to calculate M, along with these variables, quickly. Much thanks for your help.
@investor,
The fee can be written as a monthly payment, the formula for which is:
Bal = F [( 1 + r)^n -1]/r
so the entire formula is
M = PV (1+R)^N - F[(1+R)^N -1]/R
but this assumes the fee comes after the interest so you need to use N+1 in the fee formula then add back in the final payment.
M = PV (1+R)^N - F[(1+R)^(N+1) -1]/R + F
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