Calculating Compound Interest
First, the variables:
FV = future value
A = one-time investment (not for annuities)
p = investment per compound period
i = interest rate
c = number of compound periods per year
n = number of compound periods
To get
p, take the target amount to invest each month, multiply it by 12 to get a yearly investment amount, then divide by
c to get the investment per compound period. To get
n, take the number of years to invest and multiply it by
c to get the number of compound periods.
Simple compound interest with one-time investments... This is the formula that will present the future value (FV) of an investment after n years if we invest A at i interest compounded c times per year:
FV = A (1 + i/c)^{(n)}
Required current investment (A) to have FV in the future if the i interest is compounded c times per year for n years:
FV
A = -----------
(1 + i/c)^{n}
The time period (n) to have FV in the future if the initial investment A at i interest compounded c times per year:
ln(FV) - ln(A)
n = ------------------
ln(c + i) - ln(c)
NOTE: ln is the natural logarithm function.
Enter your own amounts:
Annuities are similar (but not identical) to one-time investments in all respects, except that you invest at regular intervals instead of just a one-time sum of money. For instance, investing $150.00 per month in a mutual fund.
This formula presents how much we will have (FV) after n years if we invest p per compound period at i interest compounded c times per year:
p [(1 + i/c)^{n} - 1]
FV = --------------------
(i/c)
How much is required per month (p) to reach $1 million (FV) at i interest compounded c times per year for n years?
FVi
p = -------------------
c [(1 + i/c)^{n} - 1]
How long is required (n) to reach $1 million (FV) if p monthly investments at i interest compounded c times per year:
ln(FVi + cp) - ln(cp)
n = -------------------------
ln(c + i) - ln(c)
NOTE: ln is the natural logarithm function.
Annuities: