You deposit 5000 each year into an account earning 3% interest, compounded annually. How much will you have in the account in 20 years

Answer 1

Assuming you start with no money in the account, let's begin by listing the 5 essential variables to keep track of for any annuity question:

N (number of periods) = 20 years

I/YR (interest per period) = 3% annually

PV (present value) = $0 since you start with no money in the account

PMT (payment per period) = -$5,000 (note that the payment is negative because that $5,000 is leaving your wallet every year, not because the payment itself is negative)

FV (future value) = ? (we're solving for this!)

The first way to solve for the future value using these variables is to use a financial calculator. Just plug in all of the values above into their respective keys, then click on the FV key to find a future value of $134,351.87, which is the amount you'll have in the account after 20 years.

You can also solve a question like this in Excel by using the FV function. Click on any cell in the sheet and type =FV(3%, 20, -5000) to find the same future value of $134,351.87 that we found before.

Answer: $134,351.87

Answer 2

This is a relatively common annuity type of question, and fortunately there is a formula that can solve this for us:

where FV is future value, P is the payment (deposit), r is the interest rate, and n is the number of periods

Plugging these variables in, we get:

FV = 5000 ((1.03²⁰ - 1)/.03)

FV = 134,351.87