Question

Jason wants to travel overseas in six years time. He invests R15000 in a savings account in order to save up for the overseas trip. The interest rate for the six-year period is 13% per annum compounded semi-annually. At the end of the fourth year, he runs into financial difficulty and withdraws R3000 from the account. How much money will he have saved at the end of the six-year period?​

Answer 1

R28077.05

Explanation:

The compound interest formula is:

`F = P(1 + (r)/(n))^(nt)`

where

F = future amount

r = annual interest rate

n = number of compounding periods per year

t = number of years

He invests his money for a total of 6 years, but he makes a withdrawal at the end of 4 years, so we can treat this as a 4-year investment followed by a 2-year investment.

The 4-year investment:

He invests R15000 for 4 years at 13% compounded semi-annually.

The future value at the end of the 4 years is:

`F = 15000(1 + (0.13)/(2))^(2 * 4)`

F = 24824.94

The withdrawal of R3000:

At the end of 4 years, he withdraws R3000.

R24824.94 - R3000 = R21824.94

The 2-year investment:

Now R21824.94 remains earning 13% compounded semi-annually for another 2 years.

`F = 21824.94(1 + (0.13)/(2))^(2 * 2)`

F = 28077.05

At the end of 6 years, he has R28077.05