Compound interest: the formula and how much monthly, quarterly and annual compounding differ
Compound interest is interest added to the principal so that it earns interest itself in the next period. With the same 100 million VND at the same rate, after 10 years the balance differs by tens of millions depending on whether you withdraw the interest to spend or leave it in, and by a few million more depending on whether interest is added yearly, quarterly or monthly. This article gives the formula, tables calculated exactly as the calculator at the top of this page does, the rule of 72 and a note on inflation; all interest rates are assumptions.
How compound interest differs from simple interest
Simple interest is calculated only on the original principal and is the same every year; that is what happens when you deposit money and withdraw the interest every month to spend. With compound interest, the interest is added to the principal at the end of each period, and the next period's interest is calculated on the new principal. In the first year both methods give the same figure; the difference is small for the first few years and grows over time.
| Year | Simple interest, withdrawn every year | Compound interest, added every year |
|---|---|---|
| Year 1 | Simple interest, withdrawn every year106,000,000 | Compound interest, added every year106,000,000 |
| Year 5 | Simple interest, withdrawn every year130,000,000 | Compound interest, added every year133,822,558 |
| Year 10 | Simple interest, withdrawn every year160,000,000 | Compound interest, added every year179,084,770 |
| Year 12 | Simple interest, withdrawn every year172,000,000 | Compound interest, added every year201,219,647 |
| Year 20 | Simple interest, withdrawn every year220,000,000 | Compound interest, added every year320,713,547 |
After 20 years, compound interest produces a balance almost 1.5 times that of simple interest, even though the rate and the principal are unchanged. That difference comes from leaving the interest untouched. Time is the most powerful variable in the formula, more powerful even than the interest rate, and it is also the one thing you cannot buy back.
- Doubles after
- 12 yearsAt an assumed 6% a year, by the rule of 72
- Compound interest over 10 years
- 79.1 million VND100 million at an assumed 6%, interest added yearly
- Simple interest over 10 years
- 60 million VNDSame amount, interest withdrawn every year
- Compounding period
- Monthly earns more2.85 million more on 100 million after 10 years
The compound interest formula and how to work it out yourself
Future value formula
Final balance = Initial amount × (1 + r/n) to the power of (n × t)
r is the annual interest rate as a decimal (6% is 0.06), n is the number of compounding periods per year (1 for yearly, 4 for quarterly, 12 for monthly), and t is the number of years.
Example: 100,000,000 × (1 + 0.06) to the power of 10 = 100,000,000 × 1.790848 = 179,084,770 VND.
- Convert the rate to one period
Divide the annual rate by the number of compounding periods: 6% compounded quarterly is 1.5% per period, compounded monthly 0.5%.
- Count the periods
Number of years times periods per year: 10 years compounded monthly is 120 periods.
- Raise to the power
Multiply the initial amount by (1 plus the rate per period) raised to the number of periods.
- Subtract the principal to get the interest
The final balance minus the initial amount is the compound interest earned.
On a phone calculator, enter 1.06, then the power key and 10; in Excel, multiply the amount by (1+6%)^10. With regular monthly contributions, each contribution earns interest over a different number of remaining periods, so the formula gets much longer; the calculator at the top of this page adds it up month by month so you do not have to remember it.
How much monthly, quarterly and annual compounding differ
Take the same 100 million VND at an assumed 6% a year for 10 years: adding interest every year gives 179,084,770 VND; every quarter, meaning 1.5% over 40 periods, gives 181,401,841 VND; every month, meaning 0.5% over 120 periods, gives 181,939,673 VND. The gap between monthly and yearly is 2,854,903 VND, about 1.6% of the balance. Not as large as many people think, but not a figure to ignore either.
| Compounding period | Rate per period | Periods in 10 years | Balance after 10 years | Interest |
|---|---|---|---|---|
| Yearly | Rate per period6% | Periods in 10 years10 | Balance after 10 years179,084,770 | Interest79,084,770 |
| Quarterly | Rate per period1.5% | Periods in 10 years40 | Balance after 10 years181,401,841 | Interest81,401,841 |
| Monthly | Rate per period0.5% | Periods in 10 years120 | Balance after 10 years181,939,673 | Interest81,939,673 |
"6% a year, compounded monthly" is equivalent to an effective annual rate of 6.17%; compounded quarterly, it is 6.14%. When comparing two places to put your money, convert both to the same compounding period or compare the final balances in the calculator, rather than comparing bare percentages.
Regular monthly contributions: how compound interest works over 10 years
An example calculated exactly as the calculator does it: 50 million VND to start, 3 million VND added each month, an assumed 7% a year, interest added yearly, for 10 years. The total paid in is 410 million VND; the final balance is 630,567,143 VND; the interest is 220,567,143 VND, or 35% of the balance.
| Year | Principal paid in | Accumulated interest | Year-end balance |
|---|---|---|---|
| Year 1 | Principal paid in86,000,000 | Accumulated interest6,020,000 | Year-end balance92,020,000 |
| Year 2 | Principal paid in122,000,000 | Accumulated interest14,981,400 | Year-end balance136,981,400 |
| Year 3 | Principal paid in158,000,000 | Accumulated interest27,090,098 | Year-end balance185,090,098 |
| Year 5 | Principal paid in230,000,000 | Accumulated interest61,646,053 | Year-end balance291,646,053 |
| Year 7 | Principal paid in302,000,000 | Accumulated interest111,641,966 | Year-end balance413,641,966 |
| Year 10 | Principal paid in410,000,000 | Accumulated interest220,567,143 | Year-end balance630,567,143 |
The interest column shows how it gathers pace: the first year earns just over 6 million VND, while the tenth year alone adds more than 41 million. And the lesson about time: paying in 3 million VND a month from zero at an assumed 7% gives 532 million VND after 10 years and 1.579 billion VND after 20 years, almost three times as much for only twice the money paid in. Someone who starts 10 years later has to pay in twice as much, 6 million VND a month, putting in the same 720 million VND, and after 10 years has only 1.064 billion.
The rule of 72 and inflation
The rule of 72: the number of years it takes money to double is roughly 72 divided by the interest rate in per cent. At 6% it takes 12 years (1.06 to the power of 12 is 2.012), at 8% 9 years, at 4% 18 years. The rule is accurate enough for a quick estimate while you are listening to an adviser, before you go home and open the calculator.
Inflation reduces the real value of your balance. If the interest rate is 6% and prices rise 4% a year, both of them assumptions, your purchasing power grows only about 2%; when inflation is higher than the interest rate, the balance grows while purchasing power falls. The rule of 72 works for inflation too: at 4% a year, prices double after 18 years, so long-term goals have to rise accordingly.
How the calculator works out compound interest, and the assumptions to know
The calculator adds each contribution to the balance at the start of the month and, at the end of each period, multiplies the whole balance by that period's interest. This means contributions made during a period earn the full interest for that period, slightly more than a bank that calculates by actual deposit dates; that is why, with the same 3 million VND a month, yearly compounding gives 630,567,143 VND while monthly compounding gives 622,766,475 VND. The interest rate stays the same throughout, taxes and fees are not deducted, and the maximum term is 80 years.
- Enter the initial amount, or leave it blank if you are starting from zero.
- Enter the monthly contribution and the number of years, up to 80 years.
- Enter the annual rate you are actually offered, not a more optimistic one.
- Choose the compounding period your provider uses: monthly, quarterly or yearly.
- Read the year-by-year chart of principal and interest, then try changing the number of years to see how much time matters.
Frequently asked questions
It is a method in which the previous period's interest is added to the principal so that it earns interest in the next period, unlike simple interest, which is calculated only on the original principal. The more periods and the longer the term, the larger the interest earned on interest.
At an assumed 6% with interest added yearly, the balance is 179,084,770 VND; with interest added monthly, it is 181,939,673 VND. If you withdraw and spend the interest every year, you are left with only 160 million VND including the principal.
Divide 72 by the interest rate in per cent to estimate how many years it takes money to double: about 12 years at 6%, about 9 years at 8%. The rule also works for inflation, to see how long it takes prices to double.
At the same nominal rate, yes: 6% compounded monthly is equivalent to 6.17% a year, about 2.85 million VND more on 100 million after 10 years. When comparing two places to put your money, convert both to the same compounding period.