Answer to Question #310261 in Financial Math for LINDIE

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 = 16/12 % per month = 4/3 % per month

Future Value FV = R 40,000

Deposit Per month A = R 400

Number of periods required to generate R 40,000 is n =?

$\begin{gathered} n = \ln \left( {1 + \frac{{\left( {FV \times r} \right)}}{A}} \right) \div \ln \left( {1 + r} \right) \\ n = \ln \left( {1 + \frac{{\left( {40,000 \times \frac{1}{{75}}} \right)}}{{400}}} \right) \div \ln \left( {1 + \frac{1}{{75}}} \right) \\ n = 63.97 \\ \end{gathered}$

Hence it will Kagiso to take around 64 months to get the amount R 40,000

The same has been displayed by the following table