How Much Will I Have in Savings?

Savings Account Calculator

One way to build a nest egg, house fund, or college savings fund is to deposit a fixed amount of money in a savings account every month. If you open a savings account at a credit union, or open a money market account with an online bank, you can often find annual interest rates around 3% or 4%.

To compute how much savings you will have at the end of N years, you can use the convenient savings account calculator on the left, or use the formula discussed below. If you know how much savings you will have in a given number of years, you can create a budget and a savings plan.

Savings Formula

Suppose you have an initial deposit of P dollars, an annual interest rate of r (expressed as a decimal), and you deposit D dollars in the account every month. Then the amount of money you will have at the end of N years is

                              [P + 12D/r](1 + r/12)^12N - 12D/r.

If D = 0, that is, you don't make any additional deposits, then the amount you will have at the end of N years is P(1+r)^N.

Example of How to Apply the Savings Formula

Suppose you start with a savings account balance of $4,000. If the annual interest rate is 3% and you deposit $250 in the account every month, then P = 4000, r = 0.03, and D = 250. If you want to know how much money you will have in 20 years, then you must calculate this expression:

[4000+(12)(250)/0.03](1 + 0.03/12)²⁰⁽¹²⁾ - (12)(250)/0.03
= [104000](1.0025)²⁴⁰ - 100000
= 189358 - 100000
= 89358

So in 20 years the $4,000 will grow to $89,358 as long as you deposit $250 in the account every month for 20 years.

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