Question

Tamaya purchased an ordinary annuity that earns 3.5% interest. She will receive 20 payments of $700, once a quarter over 5 years.What is the present value of the annuity?

Answer 1

The Present Value of the annuity is $9,948.68

SOLUTION

Problem Statement

The question tells us to calculate the present value of an annuity purchased by Tamay which earns 3.5% interest and requires 20 payments of $700 over a 5-year period.

Method

- There is a formula for calculating the Present Value annuity which is given below:

`\begin{gathered} PV=C*\lbrack(1-(1+i)^(-n)))/(i)\rbrack \\ \\ \text{where,} \\ C=The\text{ value of each payment} \\ i=Interest\text{ rate} \\ n=\text{ Number of times the payment is made} \end{gathered}`

- The question gave us the following parameters:

Interest rate = 3.5%

Number of payments = 20

The value of each payment = $700

- Thus, direct application of the formula given above would give us the Present Value of the annuity.

Solution

`\begin{gathered} C=700 \\ i=3.5\text{ \%}=(3.5)/(100)=0.035 \\ n=20 \\ \\ \therefore PV=C*\lbrack(1-(1+i)^(-n)))/(i)\rbrack \\ \\ PV=700*\lbrack(1-(1+0.035)^(-20))/(0.035)\rbrack \\ \\ \therefore PV=9948.68 \end{gathered}`

Final Answer

The Present Value of the annuity is $9,948.68