Savings Estimator
Estimate future savings with monthly deposits.
About the Savings Estimator
Compound interest is slow and then sudden. Most of the growth in a long savings plan happens in the final years, which is why starting early matters more than saving hard later.
How to use it
- Enter your starting balance.
- Enter what you add each month.
- Enter the rate and how many years.
The formula
Two things are growing at once: the money you started with, and each deposit you have made since. The formula adds them.
FV = P(1 + r)n + PMT × [(1 + r)n − 1] ÷ r
P is the starting balance, PMT the monthly deposit, r the monthly rate (annual ÷ 12 ÷ 100) and n the number of months. The left term compounds your lump sum; the right term is the future value of an annuity — every deposit compounding for however long it has been in the account.
The exponent is where the drama lives. Interest earns interest, so growth is not a line but a curve, and the curve is nearly flat for years before it turns steeply upward. That is not a metaphor: it is what an exponent does.
Worked examples
| Start | Monthly | Rate | Years | Deposited | Ending balance | Interest earned |
|---|---|---|---|---|---|---|
| $5,000 | $300 | 5% | 10 | $41,000 | $54,820 | $13,820 |
| $5,000 | $300 | 5% | 20 | $77,000 | $136,873 | $59,873 |
| $5,000 | $300 | 7% | 20 | $77,000 | $176,472 | $99,472 |
| $0 | $500 | 6% | 25 | $150,000 | $346,497 | $196,497 |
Compare the first two rows carefully, because they contain the whole idea. Doubling the time did not double the result. Deposits went up by 88%, and interest earned went up by 333% — from $13,820 to $59,873. The second decade earned four times what the first did, on the same monthly habit. Compounding is slow and then sudden, and almost everyone quits during the slow part.
Common mistakes
- Using a market return for a savings account. These are different products. A savings account paying 4% is not going to behave like a portfolio assumed at 8%, and planning a savings goal at an investment rate produces a number that will not arrive.
- Ignoring inflation entirely. 5% growth with 3% inflation is about 2% of real buying power. Over twenty years the nominal figure and the useful figure diverge enormously — $136,873 in 2046 does not buy what it does today.
- Forgetting tax on the interest. In a taxable account interest is usually taxed as income in the year earned, which quietly reduces the effective rate. Tax-sheltered accounts are exactly the fix for this.
- Treating the projection as a promise. A fixed rate typed into a formula is a straight line through a world that is not straight. Use it to compare choices, not to predict a balance on a particular date.
Terms explained
- Principal
- The money you put in yourself — starting balance plus every deposit. The part that is not growth.
- Compound interest
- Interest earned on interest already earned. The reason the curve bends upward instead of running straight.
- APY
- Annual percentage yield: the rate after compounding is accounted for. The right number for comparing accounts, because it is directly comparable across compounding frequencies.
- Future value
- What the account is projected to be worth at the end of the period.
- Real return
- Return after inflation. The only one that tells you what you can buy.
- Rule of 72
- Divide 72 by the rate to approximate the doubling time. At 6%, money doubles roughly every twelve years.
Common questions
- Is the rate I entered realistic?
- For a savings account, use the APY your bank actually advertises. For long-run investing, 6% to 7% after inflation is a common assumption for a diversified portfolio, and it is an assumption rather than a promise.
- Does inflation matter?
- Very much. A 5% return with 3% inflation is about 2% of real buying power. If you want a figure in today's money, enter the rate minus expected inflation.
- Monthly or annual compounding?
- Monthly compounds slightly faster, but the difference is small next to the rate and the time. Compare accounts on APY, which already includes the compounding frequency.
- Why does the interest column grow so much faster than the deposits?
- Because interest is earned on the whole balance, and the balance keeps growing. In year one there is almost nothing to earn on; by year twenty the interest alone can exceed a year of deposits.
- What matters more, the rate or the monthly amount?
- Early on, the amount you save dominates — nothing compounds if there is nothing there. Over long horizons the rate takes over. Two extra points from 5% to 7% adds $39,599 over twenty years here.
- Should I save a lump sum or spread it out?
- A lump sum invested earlier has more time to compound, so mathematically earlier wins. Spreading contributions reduces the risk of buying everything at a bad moment, which is a real consideration for investments rather than savings accounts.
- What is the Rule of 72?
- A shortcut: 72 divided by your rate approximates the years to double. At 6%, about twelve years. Useful for sanity-checking any projection in your head.
- Does this account for taxes?
- No. In a taxable account, interest is generally taxed in the year it is earned, which lowers the effective rate. Inside an ISA, IRA or 401(k) the growth is sheltered, which is most of why those accounts exist.