Compound interest is interest calculated not only on the money invested, but also on the interest that money has already earned. It is why savings grow faster and faster over the years. At the average rate paid on peso term deposits of 90 days to one year in September 2026, 4.53% a year according to the Central Bank of Chile, CLP 1,000,000 becomes $1,557,433 in 10 years and $3,777,709 in 30, if the interest is reinvested and the rate stays the same.
This guide explains the compound interest formula, how it differs from simple interest, how long money takes to double and why inflation changes the math. All examples use real rates published in Chile and the calculations are by Pauta Financiera. It is not investment advice.
View the data as a table
| 90-day to one-year term deposit | 4.53% |
| 12-month inflation | 4.1% |
| Approximate real rate | 0.41% |
| UF increase in 2026 | 3.88% |
What compound interest is
With simple interest, you earn the same each period, because the rate is always applied to the initial capital. With compound interest, each period's interest is added to the capital and, in the next period, it also earns interest. This is called compounding. In the first years the difference is small; over time it becomes huge.
An example with CLP 1,000,000 at 4.53% a year: in the first year both methods pay $45,300 of interest. But by year 10, simple interest adds up to $453,000 and compound interest to $557,433; by year 30, the difference is $1,418,709, more than the entire initial capital.
View the data as a table
| Compound interest | Simple interest | |
|---|---|---|
| 0 yrs | $1,000,000 | $1,000,000 |
| 5 yrs | $1,247,972 | $1,226,500 |
| 10 yrs | $1,557,433 | $1,453,000 |
| 15 yrs | $1,943,633 | $1,679,500 |
| 20 yrs | $2,425,599 | $1,906,000 |
| 25 yrs | $3,027,079 | $2,132,500 |
| 30 yrs | $3,777,709 | $2,359,000 |
Simple and compound interest: the difference in pesos
| Years | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | $1,045,300 | $1,045,300 | $0 |
| 5 | $1,226,500 | $1,247,972 | $21,472 |
| 10 | $1,453,000 | $1,557,433 | $104,433 |
| 20 | $1,906,000 | $2,425,599 | $519,599 |
| 30 | $2,359,000 | $3,777,709 | $1,418,709 |
Source: Pauta Financiera calculation on CLP 1,000,000 at 4.53% a year, the September 2026 average peso deposit rate for 90 days to one year from the Central Bank of Chile. Annual compounding, no taxes or fees, assuming the rate does not change over the period.
View the data as a table
| Initial capital | Interest on capital | Interest on interest | |
|---|---|---|---|
| 10 years | $1,000,000 | $453,000 | $104,433 |
| 20 years | $1,000,000 | $906,000 | $519,599 |
| 30 years | $1,000,000 | $1,359,000 | $1,418,709 |
The chart shows where the final balance comes from. After 10 years, "interest on interest" contributes just 7% of the total; after 30 years it is already the largest part of the gain, ahead of the interest on the original capital. That is why the factor that matters most in compound interest is not the rate but time.
The compound interest formula
The compound interest formula is FV = PV × (1 + i)^n, where FV is the future value, PV the initial capital, i the interest rate per period (as a decimal) and n the number of periods. If the rate is annual, n is years; if it is monthly, n is months. The interest earned is FV minus PV.
- Example: CLP 1,000,000 at 4.53% a year for 10 years: 1,000,000 × (1.0453)^10 = $1,557,433.
- Simple interest, for comparison: FV = PV × (1 + i × n). With the same data: 1,000,000 × (1 + 0.0453 × 10) = CLP 1,453,000.
- Equivalent monthly rate: (1 + annual rate)^(1/12) − 1. For 4.53% a year, it is 0.37% a month.
- In Excel or Google Sheets: =FV(rate, periods, 0, -capital) or simply =1000000*(1+0.0453)^10.
A detail about Chilean deposits: banks quote the peso rate for 30 days and calculate it as simple interest within each term. The compound effect appears when the deposit is rolled over together with its interest. We explain it with amounts and terms in our guide to how much a term deposit pays.
Does your bank, fintech or asset manager want to reach people learning how to grow their savings? Advertise on Pauta Financiera.
See advertising optionsCompound interest calculator: how much CLP 1,000,000 grows
The table below works as a compound interest calculator: it shows the final balance of CLP 1,000,000 by annual rate and number of years. The 4.12%, 4.53% and 5.26% rates are the real averages paid on peso deposits in September 2026 for 30-89 days, 90 days to one year and one to three years. The 3%, 7% and 10% rates are hypothetical, only to show the effect of the rate. Use the search box or sort by column; for another amount, scale the result proportionally.
| 3% (hypothetical) | $1,030,000 | $1,159,274 | $1,343,916 | $1,557,967 | $1,806,111 | $2,427,262 |
| 4.12% (Central Bank) | $1,041,200 | $1,223,688 | $1,497,413 | $1,832,367 | $2,242,246 | $3,357,568 |
| 4.53% (Central Bank) | $1,045,300 | $1,247,972 | $1,557,433 | $1,943,633 | $2,425,599 | $3,777,709 |
| 5.26% (Central Bank) | $1,052,600 | $1,292,162 | $1,669,682 | $2,157,498 | $2,787,837 | $4,654,799 |
| 7% (hypothetical) | $1,070,000 | $1,402,552 | $1,967,151 | $2,759,032 | $3,869,684 | $7,612,255 |
| 10% (hypothetical) | $1,100,000 | $1,610,510 | $2,593,742 | $4,177,248 | $6,727,500 | $17,449,402 |
The rule of 72: how long money takes to double
A mental shortcut for compound interest is the rule of 72: divide 72 by the annual rate and the result is roughly the number of years it takes an amount to double. At 4.53% that is about 15.9 years by the rule and 15.6 years with the exact formula. At 10%, just over seven years.
Compound interest with monthly savings
Few people invest a lump sum just once; the usual thing is to save every month. If CLP 100,000 a month is deposited at a rate equivalent to 4.53% a year, compounded monthly, after 20 years $24,000,000 will have been contributed and the balance will be $38,542,020. After 30 years, with $36,000,000 contributed, the balance reaches $75,097,217: the interest now exceeds what was saved out of pocket.
View the data as a table
| Balance with interest | Total contributed | |
|---|---|---|
| 0 | $0 | $0 |
| 5 yrs | $6,704,081 | $6,000,000 |
| 10 yrs | $15,070,586 | $12,000,000 |
| 15 yrs | $25,511,746 | $18,000,000 |
| 20 yrs | $38,542,020 | $24,000,000 |
| 25 yrs | $54,803,433 | $30,000,000 |
| 30 yrs | $75,097,217 | $36,000,000 |
| Term | Total contributed | Balance with interest | Interest earned |
|---|---|---|---|
| 5 years | $6,000,000 | $6,704,081 | $704,081 |
| 10 years | $12,000,000 | $15,070,586 | $3,070,586 |
| 15 years | $18,000,000 | $25,511,746 | $7,511,746 |
| 20 years | $24,000,000 | $38,542,020 | $14,542,020 |
| 25 years | $30,000,000 | $54,803,433 | $24,803,433 |
| 30 years | $36,000,000 | $75,097,217 | $39,097,217 |
Source: Pauta Financiera calculation with contributions of CLP 100,000 at the end of each month and a monthly rate equivalent to 4.53% a year (Central Bank of Chile, September 2026). Excludes taxes, fees and rate changes. In retirement savings, the tax benefit adds to this effect; we explain it in our guide to APV and its regimes A and B.
Compound interest and inflation: the real rate
Compound interest also works against you: inflation accumulates in the same way. The CPI rose 4.1% in the twelve months to September 2026, according to INE. With a deposit paying 4.53%, the real rate (how much purchasing power grows) is just 0.41% a year: (1.0453 ÷ 1.041) − 1. That is why long-term savings in Chile are often expressed in UF, a unit indexed to inflation. Between January 1 and November 5, 2026, the UF went from CLP 39,731.79 to CLP 41,274.20 (mindicador.cl, with SII data), an increase of 3.88%.
| Item | Value | Source |
|---|---|---|
| Peso deposit, 90 days to one year | 4.53% | Central Bank, Sep 2026 |
| Peso deposit, one to three years | 5.26% | Central Bank, Sep 2026 |
| 12-month inflation (CPI) | 4.1% | INE, Sep 2026 |
| Real rate of the one-year deposit | 0.41% | Pauta Financiera calculation |
| UF increase in 2026 (Jan 1 to Nov 5) | 3.88% | mindicador.cl / SII |
The same logic applies to riskier investments. The S&P 500 rose at a 13.5% compound annual pace over the last decade, excluding dividends, but with years of declines of up to 19%; we detail it in our article on the S&P 500 and how to invest from Chile. A higher rate speeds up compounding, but it is not guaranteed.
When compound interest works against you: debt
The same mechanism works on debts that are not paid in full: unpaid interest is added to the balance and generates new interest. That is what happens when you pay only the minimum on a credit card. To compare loans, the number that matters is the CAE (equivalent annual cost), which institutions in Chile must disclose by law and which includes interest, fees and insurance.
- Starting earlier matters more than contributing more: time is the variable with the biggest effect.
- Reinvest the interest: if it is withdrawn, the interest becomes simple again.
- Look at the real rate: a high nominal rate with high inflation may yield little.
- Fees compound too: a 1% annual cost reduces the final balance year after year.
Frequently asked questions about compound interest
What is the compound interest formula?
FV = PV × (1 + i)^n: the future value is the initial capital multiplied by one plus the period rate, raised to the number of periods. The rate and the periods must use the same unit (annual with years, monthly with months).
What is the difference between simple and compound interest?
With simple interest, interest is always calculated on the initial capital; with compound interest, also on the accumulated interest. With CLP 1,000,000 at 4.53% a year, after 30 years simple interest pays $2,359,000 and compound interest $3,777,709.
How much does CLP 1,000,000 earn with compound interest in one year?
At the September 2026 average rate for 90 days to one year (4.53%), about $45,300 before taxes. In the first period, simple and compound interest give the same result.
How do you calculate compound interest in Excel?
With the FV function (rate, periods, payment, -capital) or by typing the formula directly, for example =1000000*(1+0.0453)^10, which returns CLP 1,557,433.
Does compound interest beat inflation?
Only if the rate is higher than inflation. With a deposit at 4.53% and 12-month CPI of 4.1%, the real gain is about 0.4% a year.
Notice: this information is journalistic and educational, not financial advice. Rates change; check the terms and the total cost (CAE) with the institution before signing up.
