Copyright

Find the amount of an annuity if $290/month is paid into it for a period of 20 years, earning...

Question:

Find the amount of an annuity if [{MathJax fullWidth = 'false' \displaystyle $290/month }] is paid into it for a period of [{MathJax fullWidth = 'false' \displaystyle 20 }] years, earning interest at the rate of [{MathJax fullWidth = 'false' \displaystyle 2 \%/year }] compounded continuously. (Round your answer to the nearest whole number.)

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.

Answer and Explanation: 1

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}.


Learn more about this topic:

Loading...
What is Annuity? - Definition & Formula

from

Chapter 2 / Lesson 7

Learn about annuities. Understand what an annuity is, examine the annuity formula and learn how to calculate its future value, and see examples of annuities.


Related to this Question

Explore our homework questions and answers library