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# 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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