Question

(Solving for PMT of an annuity) To pay for your child's education, you wish to have accumulated $20,000 at the end of 9 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 14 percent compounded annually, how much must you deposit each year to reach your goal? To reach your goal, your annual deposit must be $ . (Round to the nearest cent.)

Answer 1

We can use following formula for Future value (FV) of ordinary annuity calculation (as the deposit s are made at the end on year)

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of deposit after 9 years = $20,000

PMT or deposit per year =?

And i= I/Y = 14% is the interest rate per annum

The time period n = 9 years

Therefore,

$20,000 = PMT * [(1+ 14%) ^9 -1]/ 14%

PMT = $1,243.37

To reach your goal, your annual deposit must be $1,243.37