Question

1. After a 20-year period Josh's lump sum investment matures to an amount of R313 550. How much did he invest if his money earned interest at rate of 13,65%p.a. compounded half yearly for the first 10 years, 8,4% p.a. compounded quarterly for the next five years and 7,2%p.a. compounded monthly for the remaining period?​

Answer 1

To find the initial investment, calculate the present value for each period using the compound interest formula and sum them up.

Step-by-step explanation:

To find out the initial investment, we need to find the present value using the formula for compound interest. We can break down the investment into three periods:

1. The first 10 years with a 13.65% interest rate compounded half yearly.
2. The next 5 years with an 8.4% interest rate compounded quarterly.
3. The remaining period with a 7.2% interest rate compounded monthly.

Let's calculate the present value for each period and sum them up:

• For the first period: PV = 313550/(1+(0.1365/2))^(10*2) = R69361.55
• For the second period: PV = 313550/(1+(0.084/4))^(5*4) = R183447.74
• For the third period: PV = 313550/(1+(0.072/12))^(remaining months) = R6671.14 (approx.)

Therefore, the initial investment was R69361.55 + R183447.74 + R6671.14 = R256480.43