Final answer:
To find the monthly deposit needed to save $16,000 in four years at an APR of 8.1%, use the future value of an annuity formula. Substitute the appropriate values for the future value, the monthly interest rate (APR divided by 12), and the number of payments (48). Calculate and round off to the nearest cent for practical use.
Step-by-step explanation:
To calculate the amount you need to deposit each month to save $16,000 for a down payment on a home over four years with an APR of 8.1%, you will use the future value of an annuity formula. This formula accounts for regular deposits and compound interest. Given that there are 48 months in four years, and the monthly interest rate is 0.081/12 (APR divided by 12 months), we can use the formula:
FV = P × { [(1 + r)^n - 1] / r }
where:
FV is the future value ($16,000),
P is the monthly payment,
r is the monthly interest rate,
n is the total number of payments (48).
Rearranging the formula to solve for P, and substituting the values, we will get the monthly deposit required. The result should be rounded to the nearest cent to find the most accurate and practical amount for real-world application.