Question

​(Solving

for PMT of an

annuity​)

To pay for your​ child's education, you wish to have accumulated

​$11,000

at the end of

8

years. To do this you plan on depositing an equal amount into the bank at the end of each year. If the bank is willing to pay

6

percent compounded​ annually, how much must you deposit each year to reach your​ goal?

To reach your​ goal, your annual deposit must be

​$nothing .

​(Round to the nearest​ cent.)

Answer 1

The amount to be deposited each year to reach the goal of $11,000 is calculated by using the Future Value of an Ordinary Annuity formula

Future Value of an ordinary annuity is calculated by using the following formula

Future Value of Annuity = P x [{(1+ r) ⁿ - 1} / r]

Future Value = $11,000

Interest Rate (r) = 6% per year

Number of years (n) = 8 Years

Annual Deposit (P) = ?

Future Value of Annuity = P x [{(1+ r) ⁿ - 1} / r]

$11,000 = P x [(1 + 0.06)⁸ - 1} / 0.06]

$11,000 = P x [(1.59384 – 1) / 0.06]

$11,000 = P x [0.59384 / 0.06]

$11,000 = P x 9.897467

P = $11,000 / 9.897467

P = $1,111.40

“Therefore, To reach your goal, your annual deposit must be $1,111.40”