How the savings grow
Each month your balance earns one twelfth of the annual rate, and then your deposit is added. After k months the balance is the starting savings grown at that rate plus every deposit grown for the months it has been in. Solving for the deposit or for k gives the two answers.
Balance after k months = B × (1 + r)^k + d × ((1 + r)^k − 1) ÷ r
B = saved so far, d = monthly deposit, r = annual rate ÷ 1200 (at 0%, balance = B + d × k). Deposit for a goal G in n months: d = (G − B × (1 + r)^n) × r ÷ ((1 + r)^n − 1).
Example: the deposit for a date
Goal $20,000.00 in 36 months, $2,000.00 saved, 4% a year.
- Your $2,000.00 grows by itself to $2,254.54
- Still needed: $20,000.00 − $2,254.54 = $17,745.46
- Monthly deposit: $464.77. Deposits total $16,731.54, and interest earns $1,268.46.
Example: time to reach a goal
Goal $15,000.00, $1,000.00 saved, $400.00 a month, 3% a year.
- Each month: balance × (1 + 3% ÷ 12) + $400.00
- After 33 months the balance is below $15,000.00; after 34 it is $15,264.86
- Time: 34 months (2 years 10 months)
Questions
When are deposits counted?
At the end of each month, after that month’s interest is added. A deposit made at the start of a month would earn a little more, so real results can be slightly higher.
What kind of interest rate do I enter?
A nominal annual rate, compounded monthly: one twelfth of it is added each month. If your account quotes an APY, which already includes compounding, the nominal rate is slightly lower. Enter 0 if you are not earning interest.
What does “already on track” mean?
Your current savings alone grow to the goal by the date, so no deposits are needed. The result shows what they grow to.
Does it account for taxes or inflation?
No. Interest may be taxable and prices may rise, so the goal you need may be larger than today’s figure. Adjust the goal if that matters to you.
What if the goal takes too long?
In time mode, if the deposit would take more than 100 years, or there is nothing to grow, the calculator says so and asks for a larger deposit.
Can I use it to save for a down payment?
Yes. The down payment calculator works out the down payment for a home price and then uses the same savings math to show how long saving for it takes.