How to calculate compound interest with monthly contributions
With compound interest you earn interest not only on your deposits, but also on the interest you received earlier. That makes your money grow faster and faster. See how much it adds up to with the compound interest calculator.
Simple interest vs compound interest
Say you deposit $10,000 at 5% interest per year.
- Simple interest: you earn $500 every year. After 10 years you have $15,000.
- Compound interest: in year 1 you earn $500, in year 2 5% of $10,500 = $525, in year 3 $551.25, and so on. After 10 years you have $16,288.95.
The difference of almost $1,300 is interest on interest. And it grows over time:
| Term | Simple interest | Compound interest |
|---|---|---|
| 10 years | $15,000 | $16,288.95 |
| 20 years | $20,000 | $26,532.98 |
| 30 years | $25,000 | $43,219.42 |
The formula
final balance = principal × (1 + r)^n
Here r is the interest rate per period as a decimal (5% = 0.05) and n the number of periods. For $10,000 at 5% over 10 years: 10,000 × 1.05^10 = $16,288.95.
Monthly saving: where it gets really interesting
If you put aside $200 every month at 5% a year (compounded monthly), you will have:
| Term | Total deposited | Final balance | Of which interest |
|---|---|---|---|
| 10 years | $24,000 | $31,056 | $7,056 |
| 20 years | $48,000 | $82,207 | $34,207 |
| 30 years | $72,000 | $166,452 | $94,452 |
After 30 years, more than half of your balance comes from interest. That is why starting early is so powerful: time does most of the work.
The formula with monthly contributions
With a fixed monthly contribution, use the future value of a series of deposits:
final balance = deposit × ((1 + i)^n − 1) ÷ i
Here i is the monthly rate (at 5% a year compounded monthly: 0.05 ÷ 12 = 0.4167%) and n the number of months. If you also have a starting balance, add principal × (1 + i)^n.
Worked example: $200 a month, 5% a year, 10 years (120 months): 200 × ((1.004167)^120 − 1) ÷ 0.004167 ≈ $31,056.
Year-by-year table: $200 a month at 5%
| Year | Deposited | Balance | Of which interest |
|---|---|---|---|
| 1 | $2,400 | $2,455.77 | $55.77 |
| 2 | $4,800 | $5,037.18 | $237.18 |
| 3 | $7,200 | $7,750.67 | $550.67 |
| 4 | $9,600 | $10,602.98 | $1,002.98 |
| 5 | $12,000 | $13,601.22 | $1,601.22 |
| 6 | $14,400 | $16,752.85 | $2,352.85 |
| 7 | $16,800 | $20,065.73 | $3,265.73 |
| 8 | $19,200 | $23,548.10 | $4,348.10 |
| 9 | $21,600 | $27,208.64 | $5,608.64 |
| 10 | $24,000 | $31,056.46 | $7,056.46 |
The interest earned per year keeps accelerating: about $56 in year 1, and almost $1,450 in year 10.
Realistic rates
Savings accounts may pay well below 5%, depending on where you live and the current interest climate. Investments can have higher long-term average returns, but they fluctuate and are not guaranteed. Always run a few scenarios, and remember that taxes and inflation reduce your real return.
APY: compare like with like
Banks often quote the APY (annual percentage yield) or AER, which already includes the effect of compounding. A rate of 4.9% compounded monthly equals an APY of about 5.01%. When comparing accounts, compare APYs.
Compound interest works against you too
Loans and credit cards use the same principle against you. An unpaid balance with a high interest rate grows quickly. See what a loan really costs with the loan calculator. Want to know how fast your money doubles? Read about the rule of 72.
Frequently asked questions
What is compound interest in simple terms?
Earning interest on your deposits and on the interest already added. Your balance grows faster each year.
How much is $10,000 after 10 years at 5%?
$16,288.95 with annual compounding.
Does monthly compounding make a difference?
A little. At the same rate, monthly compounding grows slightly faster than annual compounding.