Compound Interest — Formulas & Notes

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Quick recall

• Match the rate per period with the number of periods.
• Compound interest = final amount minus principal.

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Formula Cards

1. Annual compound amount

$$A=P\left(1+\frac{R}{100}\right)^T$$

2. Compound interest

$$CI=A-P$$

3. Depreciation

$$A=P\left(1-\frac{R}{100}\right)^T$$

4. Half-yearly compounding

$$A=P\left(1+\frac{R}{200}\right)^{2T}$$

Rate per period R/2; number of periods 2T.

5. Quarterly compounding

$$A=P\left(1+\frac{R}{400}\right)^{4T}$$

Rate per period R/4; number of periods 4T.

6. CI − SI over two years

$$CI-SI=P\left(\frac{R}{100}\right)^2$$

Same principal and annual rate; CI compounded annually.

Worked Examples

Example 1

Question: Rs. 10,000 earns 10% annually for 2 years, compounded annually. Find amount and CI.

Step 1: Apply the growth factor twice.

$$A=10000(1.10)^2=12100$$

Step 2: Subtract the principal.

$$CI=12100-10000=2100$$

Answer: Amount Rs. 12,100; CI Rs. 2,100.

Example 2

Question: Rs. 8,000 earns 10% annually for 1.5 years, compounded half-yearly. Find the amount.

Step 1: Convert rate and time into half-year periods.

$$\text{Rate per period}=5\%,\qquad\text{Periods}=3$$

Step 2: Apply the compound formula.

$$A=8000(1.05)^3=9261$$

Answer: Rs. 9,261.

Example 3

Question: Find CI − SI on Rs. 5,000 at 10% per year for 2 years, compounded annually.

Step 1: Use the two-year difference formula.

$$CI-SI=P\left(\frac{R}{100}\right)^2$$

Step 2: Substitute.

$$5000(0.10)^2=50$$

Answer: Rs. 50.

Drill

Try each question before opening its answer.

Question 1

P=15,000, R=8%, T=2. Find CI.

• Show answer

  2496

Question 2

P=20,000 depreciates at 10%/year for 2 years. Find value.

• Show answer

  16,200

Question 3

P=4000, R=10%, T=1 year compounded half-yearly. Find A.

• Show answer

  4410

Question 4

Difference between CI and SI on Rs.8000 at 5% for 2 years.

• Show answer

  20

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