Let's solve the problem step by step. ### Given Data: - **Future Value (FV)** = \$5,000,000 - **Interest Rate (annual, compounded quarterly)** = 6% per year - **Compounding Period (quarterly)** = every 3 months - **Number of Years (n)** = 8 years ### Step 1: Find the periodic interest rate and total number of periods. - Periodic interest rate \( i = \frac{6\%}{4} = 1.5\% = 0.015 \) - Number of periods \( N = 8 \times 4 = 32 \) quarters --- ### Step 2: Use the **Future Value of an Ordinary Annuity formula**: \[ FV = PMT \times \frac{(1 + i)^N - 1}{i} \] Where: - \( FV \) = Future value (\$5,000,000) - \( PMT \) = Periodic payment (what we want to find) - \( i \) = interest rate per period (0.015) - \( N \) = number of periods (32) Solve for \( PMT \): \[ PMT = \frac{FV \times i}{(1 + i)^N - 1} \] --- ### Step 3: Plug in the values and solve for \( PMT \): \[ PMT = \frac{5,000,000 \times 0.015}{(1.015)^{32} - 1} \] First, calculate \((1.015)^{32}\): \[ (1.015)^{32} \approx 1.63797 \] So, \[ (1.015)^{32} - 1 \approx 1.63797 - 1 = 0.63797 \] Now, \[ PMT = \frac{5,000,000 \times 0.015}{0.63797} \] \[ PMT = \frac{75,000}{0.63797} \] \[ PMT \approx 117,585.93 \] **Final answer for (A):** > The equal payment to be deposited every 3 months is **\$117,585.93**. --- ### Step 4: Calculate the total amount of interest earned (Part B): \[ \text{Total Deposits} = PMT \times N = 117,585.93 \times 32 = 3,762,749.76 \] \[ \text{Interest Earned} = FV - \text{Total Deposits} \] \[ \text{Interest Earned} = 5,000,000 - 3,762,749.76 = 1,237,250.24 \] --- ## **Summary of Answers:** **A.** The equal quarterly deposit should be **\$117,585.93**. **B.** The total interest earned in the sinking fund account is **\$1,237,250.24**.

A sinking fund involves making regular periodic payments into an account to accumulate a specified future sum, with interest compounded over time. The periodic payments are calculated using the future value of an ordinary annuity formula, considering the interest rate and number of periods.