Savings Goal Calculator

How regular saving builds up

When you save a fixed amount on a regular schedule and it earns compound returns, the total grows faster than you might expect. Each contribution starts earning its own returns, and over time those returns earn returns of their own. The formula below, called the future value of a series, captures exactly how a steady stream of deposits grows.

Here PMT is your regular deposit, r is the interest rate per period, and n is the number of deposits. The single biggest lever is time, which is why starting early matters so much.

How to use this calculator

1. Enter your regular deposit amount, written as \(PMT\).
2. Enter the interest rate per period, written as \(r\), as a decimal or as the calculator requests.
3. Enter your savings goal or target future value, written as \(FV\).
4. Click calculate to find the number of periods, \(n\), needed to reach the goal.

The formula explained

The formula \(FV = PMT \\times \\frac{(1+r)^n - 1}{r}\) computes the future value of equal deposits made at the end of each period, with interest earned each period. In this calculator, the formula is used to work backward and find how many deposits you need to reach your savings goal.

• \(\text{FV}\) = the future value, or the savings goal amount
• \(\text{PMT}\) = the regular deposit made each period
• \(r\) = the interest rate per period, written as a decimal
• \(n\) = the number of periods or deposits needed

Step by step method

1. Start with \(FV = PMT \\times \\frac{(1+r)^n - 1}{r}\).
2. Divide both sides by \(PMT\), then multiply by \(r\), so you can isolate the exponential part.
3. Use logarithms to solve for \(n\) when it is inside the exponent, because \(n\) cannot be found by ordinary arithmetic alone.

Worked example

Problem. You want to save \(5000\) dollars by depositing \(200\) dollars each month into an account earning \(0.5\\%\) per month. How many months will it take?

1. Use \(FV = PMT \\times \\frac{(1+r)^n - 1}{r}\) with \(FV = 5000\), \(PMT = 200\), and \(r = 0.005\).
2. Solve for \(n\) using logarithms, which gives \(n \\approx 23.45\).
3. Since you need a whole number of deposits, round up to \(24\) months.

Tips and common mistakes

• Make sure the interest rate matches the deposit period, for example monthly rate with monthly deposits. A yearly rate must be converted if deposits are monthly.
• If the result is not a whole number, round up, because you need one more deposit period to fully reach the goal.

Frequently asked questions