Answer to Question #311096 in Financial Math for tumi

Question

Kagiso wants to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Kagiso to have R40 000 available is

Answer 1

Solution

Interest rate $=16\%$ per year $\frac{16\%}{4}=4\%$ per quarter

Future Value $FV = R 40,000$

Deposit Per Quarter $A = R 400$

The number of periods required to generate $R 40,000$ is $n =?$

$\begin{gathered} n = \ln \left( {1 + \frac{{\left( {FV \times r} \right)}}{A}} \right) \div \ln \left( {1 + r} \right) \\ n = \ln \left( {1 + \frac{{\left( {40,000 \times \frac{4}{{100}}} \right)}}{{400}}} \right) \div \ln \left( {1 + \frac{4}{{100}}} \right) \\ n = 41.03540663 \\ \end{gathered}$

Hence it will Kagiso take around 41 quarters to get the amount of $R 40,000$

The same has been displayed by the following table