How the deposit is worked out
It answers one of two questions:
- How much to save: the smallest monthly deposit, to the cent, that gets you to the goal in the time you choose. It’s rounded up, so the goal is actually met.
- How long it takes: the month in which your balance first reaches the goal at the deposit you choose.
Behind both, the balance is followed month by month: interest is added at the monthly rate, (1 + r ÷ m)m ÷ 12 − 1 for a yearly rate r compounded m times a year, and each deposit is added at the start or end of the month. This is the same method as the Compound Interest Calculator, so the two always agree.
Without yearly increases, there’s also a formula for the deposit. With the balance growing by a monthly rate j for n months:
deposit = (goal − savings × (1 + j)n) × j ÷ ((1 + j)n − 1)
For deposits at the start of the month, divide that by (1 + j) as well. The calculator then checks the rounded-up figure against the month-by-month balance.
Worked example
The calculator’s starting values: a $30,000 goal, $5,000 saved already, 4.5% a year compounded monthly, and five years to get there.
- Monthly deposit needed: $353.58, at the end of each month
- You pay in: 60 × $353.58 = $21,214.80
- Interest earned: $3,785.50
- Balance after five years: $30,000.30, which is 30 cents over because the deposit is rounded up
Asked the other way round, saving $350 a month reaches the goal after 5 years and 1 month, and $500 a month reaches it after 3 years and 9 months.
What changes the deposit
| For the $30,000 goal | Monthly deposit |
|---|---|
| 5 years at 4.5% (the example) | $353.58 |
| 3 years instead | $631.18 |
| 10 years instead | $146.60 |
| Nothing saved yet | $446.80 |
| No interest at all | $416.67 |
Time makes the biggest difference: more months share the work, and interest has longer to add up. In the 10-year case, interest covers $7,408.60 of the goal. Depositing at the start of each month instead of the end brings the example down to $352.26. Raising the deposit 3% a year lets you start at $333.88.
Which interest rate to use
For a savings account, use the rate the bank quotes. If it’s an APY (annual percentage yield), it already includes compounding, so choose “Once a year”. Rates on savings accounts can change at any time, so check back if yours does. For money you’ll need within a few years, a guaranteed rate is a safer assumption than an investment return.
Assumptions and limitations
- The interest rate stays the same until you reach the goal.
- Deposits are made every month, on time, and nothing is withdrawn.
- Tax on interest and account fees aren’t included.
- If your goal is a price, such as a car or a deposit on a home, it may rise over time. Consider saving toward a slightly higher figure.
Questions
How is this different from the Compound Interest Calculator?
The Compound Interest Calculator starts from your deposits and shows where they end up. This one starts from where you want to end up and works out the deposit, or the time.
What if I’ve already saved enough?
The calculator says so. If your savings would reach the goal on interest alone in the time you choose, it shows that no deposit is needed.