6. Determine the regular payment for each annuity. a) An amount of 2500 is needed in 4 years by making regular.payments at the end of each month in an account that earns 4% per year, compounded monthly.

## Step 1: Convert the annual interest rate to a monthly rate.### The annual interest rate is 4%, so the monthly interest rate is .## Step 2: Calculate the number of periods.### The investment is for 4 years with monthly payments, so the number of periods is .## Step 3: Use the future value of an ordinary annuity formula.### The future value of an ordinary annuity formula is , where is the future value, is the regular payment, is the interest rate per period, and is the number of periods. We want to find , so we rearrange the formula: .## Step 4: Substitute the values and calculate the regular payment.### Substituting 2500 r = 0.003333... n = 48 PMT = 2500 \times \frac{0.003333...}{(1 + 0.003333...)^{48} - 1} \approx 2500 \times \frac{0.003333}{1.1730} \approx 2500 \times 0.002842 \approx 48.48$.