Compound Interest Formula and How to Calculate It (with Examples)
The difference from simple interest looks small in the first year and becomes large after a few years. This article covers the formula, how to calculate it step by step, and how big the gap gets in actual numbers.
Key Points
- The compound interest formula: A = P × (1 + r/n)^(n × t), where P is the principal, r the annual interest rate, n the number of compounding periods per year, and t the number of years.
- Simple interest only calculates interest on the starting principal. Compound interest calculates interest on the principal plus the interest already accumulated.
- The gap is small at first and large at the end. On Rp10 million at 8% a year, the difference is only Rp64 thousand in year two, but becomes Rp3.59 million in year ten.
- Interest compounded daily produces more than interest compounded annually, even at the same rate.
- What matters most is time, not the size of the principal. Extending the term from 10 to 20 years has a bigger impact than doubling the starting amount.
What Is Compound Interest
Imagine you deposit Rp10 million at 8% a year.
With simple interest, you receive 8% of Rp10 million every year, which is Rp800 thousand. It is always the same, because the base stays at Rp10 million.
With compound interest, you also receive Rp800 thousand in the first year. But in the second year, the 8% is calculated on Rp10.8 million, so you receive Rp864 thousand. The third year is calculated on Rp11,664,000, and so on.
The base keeps growing. That is the core of compound interest.
The Compound Interest Formula
The full formula:
A = P × (1 + r/n)^(n × t)
What each variable means:
| Symbol | Meaning | Example |
|---|---|---|
| A | Final amount, principal plus interest | what you solve for |
| P | Starting principal | Rp10,000,000 |
| r | Annual interest rate as a decimal | 8% is written 0.08 |
| n | How many times interest compounds per year | 1 (annual), 12 (monthly), 365 (daily) |
| t | Time in years | 5 |
If you only want the interest earned, not the final amount, subtract the principal:
Interest = A - P
For interest compounded once a year, the formula becomes simpler because n equals 1:
A = P × (1 + r)^t
Step-by-Step Calculation Examples
The three examples below use rupiah figures that are easy to follow. Final results are calculated from the unrounded power value, so they can differ by a few rupiah from what you get by multiplying the rounded figures in the table.
Example 1: interest compounded annually
Principal Rp10,000,000, 8% a year, 5 years, compounded once a year. That means P = 10,000,000, r = 0.08, n = 1, and t = 5.
| Step | Calculation | Result |
|---|---|---|
| 1. Fill the brackets | 1 + 0.08/1 | 1.08 |
| 2. Work out the exponent | n × t = 1 × 5 | 5 |
| 3. Raise to the power | 1.08^5 | 1.469328 |
| 4. Multiply by the principal | 10,000,000 × 1.469328 | Rp14,693,281 |
So the interest is Rp4,693,281. With simple interest, it would only be Rp4,000,000. The difference is Rp693,281.
Example 2: interest compounded monthly
Same principal and rate, but compounded every month, so n = 12.
| Step | Calculation | Result |
|---|---|---|
| 1. Fill the brackets | 1 + 0.08/12 | 1.0066667 |
| 2. Work out the exponent | 12 × 5 | 60 |
| 3. Raise to the power | 1.0066667^60 | 1.489846 |
| 4. Multiply by the principal | 10,000,000 × 1.489846 | Rp14,898,457 |
Just by changing the compounding frequency, the result grows by Rp205,176.
Example 3: a 20-year term
Principal Rp10,000,000, 8%, compounded annually, 20-year term.
| Step | Calculation | Result |
|---|---|---|
| 1. Raise to the power | 1.08^20 | 4.660957 |
| 2. Multiply by the principal | 10,000,000 × 4.660957 | Rp46,609,571 |
The principal grows more than fourfold. With simple interest, the result would only be Rp26,000,000.
Simple Interest vs Compound Interest
This is the table that explains it best. All figures use a principal of Rp10,000,000 and 8% a year, compounded annually.
| Year | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | Rp10,800,000 | Rp10,800,000 | Rp0 |
| 2 | Rp11,600,000 | Rp11,664,000 | Rp64,000 |
| 3 | Rp12,400,000 | Rp12,597,120 | Rp197,120 |
| 5 | Rp14,000,000 | Rp14,693,281 | Rp693,281 |
| 10 | Rp18,000,000 | Rp21,589,250 | Rp3,589,250 |
| 15 | Rp22,000,000 | Rp31,721,691 | Rp9,721,691 |
| 20 | Rp26,000,000 | Rp46,609,571 | Rp20,609,571 |
Note the key pattern: in year one the difference is zero, in year two it is only Rp64 thousand, but in year twenty the difference is Rp20.6 million, or twice the starting principal.
The fundamental differences:
| Simple interest | Compound interest | |
|---|---|---|
| Calculation base | Starting principal only | Principal plus accumulated interest |
| Growth | Linear, same amount each period | Exponential, growing amount each period |
| Formula | A = P × (1 + r × t) | A = P × (1 + r/n)^(n × t) |
| Commonly used in | Some loans and simple bonds | Savings, deposits, reinvestment, yield-bearing instruments |
The Effect of Compounding Frequency
At the same interest rate, the more often interest compounds, the larger the result. Here is a simulation of Rp10,000,000 at 8% over 10 years:
| Compounding frequency | n | Result after 10 years |
|---|---|---|
| Annual | 1 | Rp21,589,250 |
| Semiannual | 2 | Rp21,911,231 |
| Monthly | 12 | Rp22,196,402 |
| Daily | 365 | Rp22,253,458 |
The gap between annual and daily reaches Rp664,208. Note that the extra gain gets smaller each time the frequency goes up. From annual to monthly adds Rp607 thousand, but from monthly to daily adds only Rp57 thousand. There is an upper limit that is never exceeded, no matter how often interest compounds.
What Matters Most: Time, Not Capital
This is the most practical takeaway from all the calculations above.
Compare two scenarios at 8% compounded annually:
| Scenario | Result |
|---|---|
| Rp20,000,000 for 10 years | Rp43,178,500 |
| Rp10,000,000 for 20 years | Rp46,609,571 |
Half the principal, yet a larger result, because the time is twice as long. Doubling the starting principal doubles the result proportionally. Doubling the time makes the result multiply exponentially.
That is why with compound interest, starting earlier usually matters more than starting with more capital.
Compound Interest in Real Products
So far it has all been math. In practice, a few things make results differ from the calculations above, and they are worth knowing before you apply any of this.
Yields are usually not fixed
The formula above assumes a constant interest rate for years. For market-based instruments, the figures change with conditions. So actual results can be higher or lower than the simulation.
There are taxes and fees
The calculations above do not include tax on returns or administrative fees, both of which reduce the final result.
Inflation erodes real value
A result of Rp46.6 million in 20 years does not have the same purchasing power as Rp46.6 million today. The link between inflation and the value of money is covered in fiat money and what devaluation is.
Compounding is not always automatic
Compound interest only works if the returns are actually added back to the principal. If you withdraw them every period, what happens is simple interest.
On Mobee, this mechanism shows up in Flexi Earn, where assets you hold earn a yield that can keep accumulating, and in Dual Investment, which has a different structure with its own risk profile. For current yield figures, see the Earn product page, since the numbers change with market conditions and are not listed in this article so as not to mislead.
One thing worth stating clearly: crypto-based instruments carry price risk that conventional savings do not. An 8% annual yield means little if the underlying asset falls 30%.
Try Flexi Earn on Mobee
If you want to see how yield can keep accumulating on your assets, Flexi Earn and the other Earn products on Mobee can be a place to start, with current yield figures always shown on the product page.
Everything is in one app alongside other crypto assets, operated by PT CTXG Indonesia Berkarya, which is licensed and supervised by the Financial Services Authority (OJK), so you can hold, monitor, and manage your portfolio without switching platforms. Download and install the Mobee app now, complete verification, then start with an amount you are comfortable with.
Conclusion
The compound interest formula is A = P × (1 + r/n)^(n × t). What sets it apart from simple interest is that interest is calculated on a principal that keeps growing, not on a fixed starting amount.
The gap is small at first and large at the end. On Rp10 million at 8% a year, the difference between simple and compound interest is only Rp64 thousand in year two, but reaches Rp20.6 million in year twenty.
Two things matter most: how long the money stays invested and whether the returns are actually reinvested. A large starting principal helps, but its effect is smaller than those two factors.
Frequently Asked Questions
What is the compound interest formula?
The compound interest formula is A = P × (1 + r/n)^(n × t). A is the final amount, P the starting principal, r the annual interest rate as a decimal, n how many times interest compounds per year, and t the time in years.
What is the difference between simple and compound interest?
Simple interest is calculated only on the starting principal, so the amount is the same every period. Compound interest is calculated on the principal plus the interest already accumulated, so the amount keeps growing.
How do you calculate compound interest?
Put the principal, interest rate, compounding frequency, and time into A = P × (1 + r/n)^(n × t). For example, Rp10,000,000 at 8% a year for 5 years, compounded annually, becomes about Rp14,693,281.
What does n mean in the compound interest formula?
n is how many times interest compounds in one year. It is 1 for annual, 2 for semiannual, 12 for monthly, and 365 for daily.
Is daily or annual compounding better?
At the same interest rate, daily compounding produces more than annual compounding. But the extra gain gets smaller each time the frequency increases, and there is an upper limit that is never exceeded.
Are yields on Mobee guaranteed like the calculations in this article?
No. The numbers in this article are illustrations only. Yields on products such as Flexi Earn can change with market conditions, and crypto assets carry price risk. See current figures on the Earn product page.
Disclaimer
All information in this article is educational and is not investment advice. The figures in the calculation examples are illustrative and are not a yield projection for any product. Actual returns can differ, and crypto-based instruments carry price fluctuation risk. Always do your own research and match decisions to your own risk profile. Mobee is operated by PT CTXG Indonesia Berkarya, licensed and supervised by the Financial Services Authority (OJK).
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