1. **State the problem:** We want to find the quarterly deposit amount needed so that after 5 years, with interest compounded quarterly at 7.5% per year, the company will have R900000. 2. **Identify variables and formulas:** - Future value needed, $FV = 900000$ - Annual interest rate, $r = 7.5\% = 0.075$ - Compounded quarterly, so interest rate per quarter, $i = \frac{0.075}{4} = 0.01875$ - Number of quarters in 5 years, $n = 5 \times 4 = 20$ - Deposit amount per quarter = $P$, which is what we want to find. 3. **Use the formula for the future value of an ordinary annuity:** $$FV = P \times \frac{(1+i)^n - 1}{i}$$ Rearranged to solve for $P$: $$P = \frac{FV \times i}{(1+i)^n - 1}$$ 4. **Calculate denominator:** $$ (1+i)^n - 1 = (1 + 0.01875)^{20} - 1 = 1.01875^{20} - 1 $$ Calculate $1.01875^{20}$: $$ 1.01875^{20} \approx 1.45144 $$ So, $$1.45144 - 1 = 0.45144$$ 5. **Calculate $P$:** $$ P = \frac{900000 \times 0.01875}{0.45144} = \frac{16875}{0.45144} \approx 37368.96 $$ 6. **Interpretation:** The company needs to deposit approximately R37368.96 at the end of every quarter starting in 3 months to haveR900000 in the fund after 5 years.