Answer to Question #311099 in Financial Math for BAZAR

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

A.

28 quarters.

B.

41 quarters.

C.

40 quarters.

D.

12 quarters.

Answer 1

Solution

Interest rate = 16% per year = 16/4 % per quarter = 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