How much would you need to deposit in an account each month in order to have $10,000 in the account in 8 years? Assume the account earns 8% interest.

Question

How much would you need to deposit in an account each month in order to have $10,000 in the account in 8 years? Assume the account earns 8% interest.

Answer 1

Time value of money is the reason we cannot compare cash flows across different time periods. They must first be discounted by their required rate of return (interest rate). The easiest way to solve is to use the financial functions on the calculator. It asks for the monthly payment, so we need to adjust the time period (n) and the interest rate (i) to reflect monthly payments. Monthly payments over 8 years results in

N=8(12)=96

I/Y=(8/12)=0.666666667

Now we can use the financial functions on the calculator to solve for the monthly payment amount.

N=96, I/Y=0.666666667, FV=10,000, compute PMT

PMT= $74.70

You would deposit $74.70 each month.

Another way to approach this is by using the Future Value of Annuity Formula

FVA=PMT x FVIFA _i,n

Where FVIFA represents the Future Value Interest Factor of Annuity.

We can use a FVIFA table or you can find it using your calculator

N=96, I/Y=.666666667, PMT= -1, Compute FV

FVIFA=133.868583

FVA=PMT x FVIFA _i,n

10,000=PMT x 133.868583

Divide both sides by 133.868583

10,000 / 133.868583 = PMT = $74.70