Respuesta :
Answer
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:
[tex]\begin{gathered} PV=C\times\lbrack\frac{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}[/tex]- 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
[tex]\begin{gathered} C=700 \\ i=3.5\text{ \%}=\frac{3.5}{100}=0.035 \\ n=20 \\ \\ \therefore PV=C\times\lbrack\frac{1-(1+i)^{-n})}{i}\rbrack \\ \\ PV=700\times\lbrack\frac{1-(1+0.035)^{-20}}{0.035}\rbrack \\ \\ \therefore PV=9948.68 \end{gathered}[/tex]
Final Answer
The Present Value of the annuity is $9,948.68
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