Determine the regular monthly payment required to have 5000 at the end of 4 years if the investment earns 5.3% interest, compounded monthly. Select one: a. 93.74 b. 86.03 C. 89.61 d. 95.22

## Step 1: Convert the annual interest rate to a monthly rate.<br />### The annual interest rate is 5.3%, so the monthly interest rate is $\frac{5.3\%}{12} = \frac{0.053}{12} \approx 0.00441667$.<br /><br />## Step 2: Calculate the number of compounding periods.<br />### The investment is compounded monthly for 4 years, so the number of periods is $4 \times 12 = 48$.<br /><br />## Step 3: Use the future value of an ordinary annuity formula.<br />### The future value of an ordinary annuity formula is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value, $P$ is the periodic payment, $r$ is the periodic interest rate, and $n$ is the number of periods. We want to find $P$, so we rearrange the formula: $P = FV \times \frac{r}{(1 + r)^n - 1}$.<br /><br />## Step 4: Plug in the values and solve for P.<br />### $P = 5000 \times \frac{0.00441667}{(1 + 0.00441667)^{48} - 1} \approx 5000 \times \frac{0.00441667}{1.23656 - 1} \approx 5000 \times \frac{0.00441667}{0.23656} \approx 5000 \times 0.018670 \approx 93.35$.