1. **State the problem:** We want to find the amount to deposit at the end of each quarter in a savings fund with 8% annual interest compounded quarterly to have 100000 after 5 years. 2. **Formula used:** The future value of an ordinary annuity compounded periodically is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $FV$ is the future value (100000), - $P$ is the payment per period (what we want to find), - $r$ is the interest rate per period, - $n$ is the total number of payments. 3. **Calculate parameters:** - Annual interest rate = 8% = 0.08 - Compounded quarterly means 4 periods per year, so $$r = \frac{0.08}{4} = 0.02$$ - Number of years = 5, so total payments: $$n = 5 \times 4 = 20$$ 4. **Plug values into formula:** $$100000 = P \times \frac{(1 + 0.02)^{20} - 1}{0.02}$$ 5. **Calculate the numerator:** $$ (1 + 0.02)^{20} = 1.02^{20} \approx 1.485947$$ 6. **Calculate the fraction:** $$ \frac{1.485947 - 1}{0.02} = \frac{0.485947}{0.02} = 24.29735$$ 7. **Solve for $P$:** $$P = \frac{100000}{24.29735} \approx 4117.14$$ **Final answer:** You should deposit approximately **4117.14** at the end of each quarter to have 100000 after 5 years.