## Annuities:

An annuity is a term used in financial management that deals with a series payments under a contract. There are three main types of annuities: fixed annuity, indexed variable annuity, and variable annuity.

Given Data:

• The payment for the annuity is 290 dollars per month.
• The time period is 20 years.
• The rate of interest is 2% per year, compounded continuously.

The expression for determining the amount of the annuity is given as:

{eq}A = \dfrac{{R\left( t \right)}}{r}\left( {{e^{rT}} - 1} \right){/eq}

Here, {eq}R\left( t \right){/eq} is the payment rate, {eq}r{/eq} is the rate of interest and {eq}T{/eq} is the time period.

Since the payment is given in terms of month, we need to convert it into yearly payments:

{eq}\begin{align*} R\left( t \right)& = 290 \times 12\\ R\left( t \right)& = 3480 \end{align*}{/eq}

Substitute 3480 for {eq}R\left( t \right){/eq}, 0.02 for {eq}r{/eq} and 20 for {eq}T{/eq} in the above equation to determine the amount of the annuity.

{eq}\begin{align*} A& = \dfrac{{3480}}{{0.02}}\left( {{e^{0.02 \times 20}} - 1} \right)\\ A &= 174000\left( {{e^{0.4}} - 1} \right)\\ A &= 85577.5 \end{align*} {/eq}

Thus, the annuity is worth {eq}\$85,577.50 {/eq}.