Two ways interest can build
Simple interest is calculated only on the original amount. Compound interest is calculated on the original amount plus any interest already earned, so the base grows each period.
The difference looks small in the first year and becomes large over decades. That is why time, not just rate, is the most powerful input in a long-term plan.
Key points
- Simple interest: earn on the principal only.
- Compound interest: earn on principal and on past interest.
- The gap widens with both the rate and the number of periods.
The two growth paths
FV = PV × (1 + r × n)
Interest is paid on the original principal only.
FV = PV × (1 + r)ⁿ
Each period earns interest on the previous balance.
The compounding advantage is the compound future value minus the simple future value. Reading the interest rate as a decimal (8% is 0.08) keeps the arithmetic clean.
Same rate, different results
Invest ৳10,000 for 3 years at 8%. Simple interest pays ৳800 each year, giving ৳12,400 in total. Compound interest multiplies the balance: ৳10,000 × 1.08³ = ৳12,597.12.
The ৳197 gap is the interest earned on the first two years of interest. Over 30 years at the same rate the compound balance is more than double the simple one.
Putting it to work
Fixed deposits and simple loans often quote simple interest. Savings accounts, index funds, and credit-card balances compound. Credit cards compound against you, which is why unpaid balances grow so quickly.
Ask how often interest compounds. Annual, monthly, and daily compounding give different results. The more often interest is added, the faster the balance grows.
Key points
- Compounding rewards patient, long-horizon saving.
- On debt it works against you just as efficiently.
- Check the compounding frequency before comparing products.
02 / Calculate
Watch value compound.
Change the starting amount, the rate, or the horizon. A negative rate models inflation and shows the loss of buying power.
An annual ৳100,000 grows at 8% for 15 years with no extra contributions.
Future value
৳317,216.91
After 15 years the balance is ৳3.17 L. You contributed ৳100,000.00 and earned ৳217,216.91 in growth.
Total interest earned
৳217,216.91
Compounding vs simple interest
+৳97,216.91
Year by year
| Year | Opening | Added | Growth | Closing |
|---|---|---|---|---|
| 1 | ৳100,000.00 | ৳0.00 | ৳8,000.00 | ৳108,000.00 |
| 2 | ৳108,000.00 | ৳0.00 | ৳8,640.00 | ৳116,640.00 |
| 3 | ৳116,640.00 | ৳0.00 | ৳9,331.20 | ৳125,971.20 |
| 4 | ৳125,971.20 | ৳0.00 | ৳10,077.70 | ৳136,048.90 |
| 5 | ৳136,048.90 | ৳0.00 | ৳10,883.91 | ৳146,932.81 |
| 6 | ৳146,932.81 | ৳0.00 | ৳11,754.62 | ৳158,687.43 |
| 7 | ৳158,687.43 | ৳0.00 | ৳12,694.99 | ৳171,382.43 |
| 8 | ৳171,382.43 | ৳0.00 | ৳13,710.59 | ৳185,093.02 |
| 9 | ৳185,093.02 | ৳0.00 | ৳14,807.44 | ৳199,900.46 |
| 10 | ৳199,900.46 | ৳0.00 | ৳15,992.04 | ৳215,892.50 |
| 11 | ৳215,892.50 | ৳0.00 | ৳17,271.40 | ৳233,163.90 |
| 12 | ৳233,163.90 | ৳0.00 | ৳18,653.11 | ৳251,817.01 |
| 13 | ৳251,817.01 | ৳0.00 | ৳20,145.36 | ৳271,962.37 |
| 14 | ৳271,962.37 | ৳0.00 | ৳21,756.99 | ৳293,719.36 |
| 15 | ৳293,719.36 | ৳0.00 | ৳23,497.55 | ৳317,216.91 |
Test the assumption
What if the rate changes?
The same inputs, compared across nearby rates.
6.0% rate
৳239,655.82
Comparison scenario
8.0% rate
৳317,216.91
Your current assumption
10.0% rate
৳417,724.82
Comparison scenario
Growth uses a constant annual rate with interest added once a year. Contributions are added at each year-end. Real products compound more often and carry fees, taxes, and risk.
03 / Apply
Choosing between two deposits
One bank offers simple interest at 8% for 3 years. Another offers 8% compounded annually. A saver with ৳10,000 wants to know which pays more and by how much.
The assumptions
- Both accounts hold the money for exactly 3 years.
- No money is withdrawn and no fees are charged.
- The quoted rate is the same for both products.
What to take away
01
Compounding wins whenever interest stays invested.
02
The advantage is small at first and grows with time.
Your turn
0 of 3 answered
01Question
Using simple interest, what does ৳10,000 grow to after 3 years at 8%?
02Question
Using compound interest, what does ৳10,000 grow to after 3 years at 8%? Round to two decimals.
03Question
Which statement best explains why compounding pulls ahead over time?
Take it into the Lab
Experiment with the same idea.
The Lab turns this topic into a workspace: change the drivers, watch the statements move, and see the consequence before you commit to a decision.
What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
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Open the playgroundSources & further reading
OpenStax · Principles of Finance (free textbook) ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.