Question

Calculate annuity cash flows

Your goal is to have $20,000 in your bank account by the end of nine years. If the interest rate remains constant at 10% and you want to make annual identical deposits, you'll have to deposit (1,325.53, 1178.25, 1767.37, 1030.97,1472.81, or 1620.09) into your account at the end of each year to reach your goal.
If your deposits were made at the beginning of each year rather than an at the end, the amount of your deposit would change by (133.89, 113.81, 180.75, 167.36, 127.20, or 100.42) if you still wanted to reach your financial goal by the end of nine years.

Answer 1

Annual deposit amount for an ordinary annuity and an annuity due that will result in $20,000 at 10% interest over nine years, use the future value annuity formulas. Once the ordinary annuity payment is found, adjust it for the annuity due by accounting for one additional interest period.

Step-by-step explanation:

To calculate annuity cash flows and achieve your financial goal of having $20,000 in your bank account by the end of nine years with a constant interest rate of 10%, you would use the formula for the future value of an annuity. The formula for the future value of an annuity due (payments made at the beginning of each period) differs from an ordinary annuity (payments made at the end of each period), because each payment in an annuity due earns interest for one additional period.

To find out how much you need to deposit annually, you would need to determine which of the provided values correctly fulfills the equation for the future value of an ordinary annuity or an annuity due. As the problem provides multiple options, one approach is to use the present value of annuity formula to reverse-engineer the correct deposit.

The formula for the future value of an ordinary annuity is:
Future Value = Pmt × × ((1 + r)n - 1) / r
Where Pmt is the payment amount per period, r is the interest rate per period, and n is the number of periods.

Once you identify the correct payment, the change in deposit amount if shifted to an annuity due can be calculated by multiplying the ordinary annuity payment by (1 + r) to account for the additional interest period gained by depositing at the beginning of the year.