Why compound interest matters for a 10th grader
Ever wondered why a small amount of money can grow into a big sum over time? That magic is called compound interest, and it shows up in many exam questions.
💡 In Simple Words: Compound interest means you earn interest on the original money *and* on the interest you’ve already earned. Think of it like a snowball rolling down a hill – it picks up more snow (interest) as it rolls (time).
What is compound interest?
Compound interest is the extra money you get when the interest itself starts earning interest. The key ingredients are:
- Principal (P): the starting amount of money.
- Rate (r): the percentage you earn each year, written as a decimal.
- Time (t): how many years the money stays invested.
- Compounding frequency (n): how many times a year the interest is added (yearly, half‑yearly, quarterly, monthly).
The formula that ties them together is:
A = P (1 + r/n)^(n·t)
Here A is the total amount after t years, including the interest.
How to calculate compound interest – step by step
Follow these four easy steps whenever you see a problem.
- Read the question and note down P, r, t and n.
- Convert the rate from a percent to a decimal (divide by 100).
- Plug the numbers into the formula
A = P(1 + r/n)^(n·t). - Do the arithmetic: first the bracket, then raise to the power, finally multiply by P. If the question asks for just the interest, subtract P from A.
Worked example – a typical Class 10 question
Question: Rahul deposits ₹5,000 in a bank that pays 8% interest per year, compounded quarterly. How much will he have after 3 years?
Step 1 – Identify the values
- P = 5,000
- r = 8% = 0.08
- t = 3 years
- n = 4 (quarterly means four times a year)
Step 2 – Put them into the formula
A = 5,000 (1 + 0.08/4)^(4·3)
First simplify inside the bracket: 0.08/4 = 0.02, so (1 + 0.02) = 1.02.
Now the exponent: 4·3 = 12, so we need 1.02¹².
Using a calculator, 1.02¹² ≈ 1.26824.
Finally multiply: A ≈ 5,000 × 1.26824 = ₹6,341.20.
So Rahul will have about ₹6,341 after three years.
If the exam asks for the interest only, subtract the principal: 6,341.20 – 5,000 = ₹1,341.20.
Another quick example – annual compounding
Question: A sum of ₹2,000 is invested at 5% per annum, compounded annually. Find the amount after 5 years.
Here n = 1 (once a year). Plugging in:
A = 2,000 (1 + 0.05/1)^(1·5) = 2,000 (1.05)⁵ ≈ 2,000 × 1.27628 = ₹2,552.56.
Interest earned = ₹552.56.
Simple vs. compound interest – a quick comparison
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| What grows? | Only the principal. | Principal + previous interest. |
| Formula | I = P r t | A = P(1 + r/n)^(n·t) |
| Typical use in exams | Basic word problems. | Multi‑step questions, higher marks. |
| Effect over time | Linear increase. | Exponential increase (gets steeper). |
Common pitfalls and how to avoid them
- Forgetting to convert % to decimal. 8% → 0.08, not 8.
- Mixing up n and t. n is how many times per year; t is years.
- Skipping the parentheses. The whole (1 + r/n) must be raised to the power n·t.
- Rounding too early. Keep extra decimals until the final answer.
📝 Likely Exam Questions
- Question: A sum of ₹10,000 is placed in a bank at 12% per annum, compounded half‑yearly. Find the amount after 2 years.
Answer: n = 2, r = 0.12, t = 2.
A = 10,000(1 + 0.12/2)^(2·2) = 10,000(1.06)⁴ ≈ ₹13,384. - Question: Calculate the compound interest on ₹7,500 for 4 years at 9% per annum, compounded annually.
Answer: A = 7,500(1 + 0.09)⁴ ≈ ₹10,497. Interest = ₹10,497 – 7,500 = ₹2,997. - Question: A deposit of ₹3,200 earns 6% interest, compounded monthly. What is the total amount after 18 months?
Answer: n = 12, t = 1.5 years.
A = 3,200(1 + 0.06/12)^(12·1.5) ≈ 3,200(1.005)¹⁸ ≈ ₹3,600. - Question: If the amount after 5 years is ₹9,000 and the rate is 10% compounded yearly, what was the original principal?
Answer: A = P(1.10)⁵ ⇒ P = 9,000 / (1.10)⁵ ≈ ₹5,585.