Compound Interest & Growth
Financial Applications: Compound Interest & Growth
Compound Interest & Growth
Compound Interest & Growth
What you'll learn
- How compound interest differs from simple interest.
- Using the compound interest formula to solve real-world problems.
- Modelling inflation and population growth using exponential functions.
Key concepts
Simple vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest on | Principal only | Principal + accumulated interest |
| Growth | Linear | Exponential |
| Formula | I = P × r × t | A = P(1 + r/n)^(nt) |
Compound Interest Formula
A = P(1 + r/n)^(nt)
| Variable | Meaning |
|---|---|
| A | Final amount |
| P | Principal (initial investment) |
| r | Annual interest rate (decimal) |
| n | Times compounded per year |
| t | Time in years |
Special case — annually (n=1): A = P(1 + r)^t
Example: ₹10,000 at 8% p.a. compounded annually for 3 years:
- A = 10,000 × (1.08)³ = 10,000 × 1.2597 = ₹12,597
Continuous Compounding
When compounding frequency → ∞: A = Pe^(rt)
Used in advanced finance, population models, radioactive decay.
Inflation
Inflation erodes purchasing power:
- Real value = Nominal amount ÷ (1 + inflation rate)^t
- If inflation = 6% and you have ₹1,00,000 today, in 10 years its real value = ₹1,00,000 ÷ (1.06)^10 ≈ ₹55,839
Doubling Time — Rule of 72
Doubling time ≈ 72 ÷ (interest rate %)
- At 8% interest: doubles in ≈ 9 years.
- At 12% interest: doubles in ≈ 6 years.
Growth and Decay Models
| Model | Formula | Example |
|---|---|---|
| Population growth | P = P₀(1 + r)^t | City population |
| Asset depreciation | V = V₀(1 − r)^t | Car value |
| Radioactive decay | N = N₀(½)^(t/T½) | Carbon dating |
Quick check
- What is the difference between simple and compound interest?
- Calculate the compound interest on ₹5,000 at 10% p.a. for 2 years (annual compounding).
- Using Rule of 72, how many years to double at 6% interest?
- If inflation is 5% p.a., what will ₹50,000 be worth in 5 years in today's money?
Open the Practice tab for graded questions on Compound Interest & Growth.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Quick check
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