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\[I = Prn\]

Where:

I = Interest

P = Principal (original) amount

r = Interest rate per period of time expressed as a decimal

n = Number of periods

I = Interest

P = Principal (original) amount

r = Interest rate per period of time expressed as a decimal

n = Number of periods

\[A = P(1 + r)^n\]

Where:

A = Final amount

P = Principal (original) amount

r = Interest rate per period of time expressed as a decimal

n = Number of time periods

A = Final amount

P = Principal (original) amount

r = Interest rate per period of time expressed as a decimal

n = Number of time periods

An **annuity** is an investment where **equal amounts** are contributed to an account at **regular intervals**.

The present value of an annuity is the amount of money that could be
invested now (at the same rate of a compound interest for the same length of time)
to give the same result as an annuity with regular contributions, M.

Future value

\[FV = M\left[\frac{(1 + r)^n - 1}{r} \right]\]
Where:

FV = Future value of an annuity

M = Contribution per period (paid at the end of the period)

r = Interest rate per period of time expressed as a decimal

n = Number of periods

FV = Future value of an annuity

M = Contribution per period (paid at the end of the period)

r = Interest rate per period of time expressed as a decimal

n = Number of periods

Present value

\[\begin{eqnarray*} PV &=& \frac{FV}{(1+r)^n} \\\\ &=& M\left[\frac{(1 + r)^n - 1}{r(1+r)^n} \right] \\\\ &=& M\left[\frac{ 1 - (1 + r)^{-n}}{r} \right] \end{eqnarray*}\]