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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:

 Finding the future value of a one-time investment Investment: Interest rate: number of times compounded each year: Number of years: Result:

 Finding the one-time investment neededto reach a desired future value Desired future value: Interest rate: Number of times compounded each year: Number of years: Result:

 Finding the number of years it will take toreach a desired future value Desired future value: Investment: Interest rate: Number of times compounded each year: Result:

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:

 Finding the future value of an annuity Investment per month: Interest rate: Number of times compounded each year: Number of years: Result:

 Finding the investment per month needed in anannuity to reach a desired future value Desired future value: Interest rate: Number of times compounded each year: Number of years: Result:

 Finding the number of years it will take to reacha desired future value in an annuity Desired future value: Investment per month: Interest rate: Number of times compounded each year: Result: 