Maths / Quantative Ability: Simple Interest & Compound Interest NOTES AND PRACTICE QUESTIONS

  Interest is the extra money paid by a borrower to the lender for using money for a certain period. There are two types of interest:

1. Simple Interest (SI)
2. Compound Interest (CI)

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1) Simple Interest (SI)

Simple Interest is calculated on the principal (original amount) for the entire period.

Formula for Simple Interest:

$$SI=\frac{P\times R\times T}{100}$$

Where:

• P = Principal amount (Initial money)
• $R$ = Rate of interest per year (%)
• $T$ = Time in years

Total Amount (A) After SI:

$$A=P+SI$$

Example 1: Basic Simple Interest Calculation

Q: A person invests ₹5000 at an interest rate of 10% per annum for 3 years. What will be the simple interest earned?

Solution:

$$SI=\frac{5000\times 10\times 3}{100}=\text{₹}1500$$

Total Amount = ₹5000 + ₹1500 = ₹6500

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2) Compound Interest (CI)

Compound Interest is calculated on the principal plus the interest earned in previous periods.

Formula for Compound Interest:

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

Where:

• $A$ = Final Amount
• $P$ = Principal
• $R$ = Rate of Interest
• $T$ = Time in years

Formula for Compound Interest (CI) Only:

$$CI=A-P$$

Example 2: Basic Compound Interest Calculation

Q: A person invests ₹5000 at 10% annual interest for 3 years. What will be the compound interest?

Solution:

$$A = 5000 \left(1 + \frac{10}{100}\right)^3$$
$$= 5000 \times \left(1.1\right)^3$$
$$= 5000 \times 1.331 = ₹6655$$
$$CI = ₹6655 - ₹5000 = ₹1655$$

3) Differences Between SI and CI

4) Common Question Types for Exams

Type 1: Find Simple Interest

Q: Find the simple interest on ₹6000 at 8% per annum for 5 years.
Solution:

$$SI=\frac{6000\times 8\times 5}{100}=\text{₹}2400$$

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Type 2: Find Compound Interest

Q: Find the compound interest on ₹4000 at 5% per annum for 2 years.
Solution:

$$A = 4000 \left(1 + \frac{5}{100}\right)^2$$
$$= 4000 \times 1.1025 = ₹4410$$
$$CI = ₹4410 - ₹4000 = ₹410$$

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Type 3: Difference Between SI and CI

Q: Find the difference between SI and CI on ₹5000 for 2 years at 10% per annum.

Solution:

1. SI Calculation:

$$SI = \frac{5000 \times 10 \times 2}{100} = ₹1000$$

2. CI Calculation:

$$A = 5000 \left(1 + \frac{10}{100}\right)^2$$
$$= 5000 \times 1.21 = ₹6050$$
$$CI = ₹6050 - ₹5000 = ₹1050$$

                                                      Difference = ₹1050 - ₹1000 = ₹50

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Type 4: Find the Rate of Interest

Q: ₹8000 becomes ₹9680 in 3 years under SI. Find the rate of interest.

Solution:

$$SI = A - P = 9680 - 8000 = ₹1680$$
$$1680 = \frac{8000 \times R \times 3}{100}$$$$R = \frac{1680 \times 100}{8000 \times 3} = 7\%$$

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Type 5: Find Time Period

Q: How many years will ₹5000 take to become ₹6500 at 10% per annum under SI?

Solution:

$$SI = 6500 - 5000 = ₹1500$$
$$1500 = \frac{5000 \times 10 \times T}{100}$$$$T = \frac{1500 \times 100}{5000 \times 10} = 3 \text{ years}$$

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Type 6: Half-Yearly and Quarterly CI

Formula:
For half-yearly interest, divide the rate by 2 and double the time:

$$A = P \left(1 + \frac{R/2}{100}\right)^{2T}$$

For quarterly interest, divide the rate by 4 and multiply the time by 4:

$$A = P \left(1 + \frac{R/4}{100}\right)^{4T}$$

Example:
Find the compound interest on ₹6000 at 8% per annum for 1 year, compounded half-yearly.

Solution:

$$A = 6000 \left(1 + \frac{8/2}{100}\right)^2$$
$$= 6000 \times (1.04)^2$$
$$= 6000 \times 1.0816 = ₹6489.6$$
$$CI = ₹6489.6 - ₹6000 = ₹489.6$$

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Conclusion & Shortcuts

1. If SI and CI are asked for 1 year, both are the same.
2. If the difference between SI and CI is asked for 2 years, use: $$\text{Difference} = P \times \left(\frac{R}{100}\right)^2$$
   
3. If the difference between SI and CI is asked for 3 years, use: $$\text{Difference} = P \times \left(\frac{R}{100}\right)^2 \times \left(\frac{3R + 100}{100}\right)$$

   I. Simple Interest (SI) Questions

   Level 1: Basic Questions

   1. A sum of Rs. 5000 is lent at an interest rate of 8% per annum for 5 years. Find the simple interest.
   2. If the simple interest on a sum for 4 years at 6% per annum is Rs. 720, find the principal amount.
   3. A sum becomes Rs. 2400 after 4 years at an interest rate of 5% per annum. Find the original principal.
   4. At what rate of interest will Rs. 2500 yield Rs. 500 as simple interest in 5 years?
   5. A person borrowed Rs. 8000 at 9% p.a. for 3 years. How much total amount does he have to repay?

   Level 2: Moderate Questions

   6. The difference between the simple interest on Rs. 6000 for 4 years and Rs. 5000 for 3 years at the same rate is Rs. 480. Find the rate of interest.
   7. A sum of Rs. X earns Rs. 5400 as simple interest in 6 years at an annual rate of 9%. Find X.
   8. If the simple interest on a sum for 2 years at 7% per annum is Rs. 1540, find the principal amount.
   9. A certain sum amounts to Rs. 8400 in 5 years at a simple interest rate of 4% per annum. Find the principal.
   10. A person deposits Rs. 10,000 in a bank at 10% p.a. SI for 6 years. How much interest will he earn?

   Level 3: Advanced Questions

   11. A sum of Rs. 15,000 is split into two parts such that one part is lent at 8% p.a. and the other at 10% p.a. If the total interest after 3 years is Rs. 4050, find both parts.
   12. The simple interest on a sum for 5 years at R% p.a. is 80% of the principal. Find R.
   13. The sum of money becomes 5 times in 20 years at simple interest. Find the rate of interest.
   14. A sum of Rs. 4,000 is invested in two schemes. One gives 5% SI and the other 8% SI. The total interest earned in 4 years is Rs. 1,120. How much was invested in each scheme?
   15. A sum is borrowed at 12% per annum SI for 7 years. The total interest paid is Rs. 6300. Find the principal.

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   II. Compound Interest (CI) Questions

   Level 1: Basic Questions

   1. Find the compound interest on Rs. 5000 at 10% p.a. for 2 years.
   2. If Rs. 6400 grows to Rs. 7744 in 2 years at CI, find the rate of interest.
   3. A sum of Rs. 5000 is invested at 8% p.a. CI for 3 years. Find the amount.
   4. What will be the compound interest on Rs. 8000 for 2 years at 5% per annum?
   5. A sum of Rs. 4000 amounts to Rs. 4410 in 2 years under compound interest. Find the rate of interest.

   Level 2: Moderate Questions

   6. A sum of money becomes 1.44 times in 2 years under compound interest. Find the annual rate.
   7. A sum of Rs. 10000 earns Rs. 3152 as CI in 2 years. Find the rate of interest.
   8. The difference between simple and compound interest on Rs. 5000 for 2 years at 10% p.a. is Rs. 50. Verify this.
   9. A sum of Rs. 12000 grows to Rs. 13464 in 2 years under CI. Find the rate of interest.
   10. If Rs. 5000 becomes Rs. 6050 in 2 years, find the annual rate of CI.

   Level 3: Advanced Questions

   11. A sum of Rs. 20,000 is invested at 5% p.a. CI. Find the amount after 3 years if interest is compounded half-yearly.
   12. The population of a city increases at 8% p.a.. If the current population is 1,25,000, find the population after 3 years.
   13. A sum becomes Rs. 19,448 in 3 years under compounded annually at 12% per annum. Find the principal.
   14. Find the difference between compound and simple interest on Rs. 6000 for 2 years at 8% per annum.
   15. A person invests Rs. 5000 in a scheme that offers 6% CI quarterly. Find the amount after 1 year.

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   III. Mixed SI & CI Questions

   1. A sum of Rs. 8000 earns Rs. 9600 in 2 years under simple interest. How much will the same sum earn in 2 years under CI at the same rate?
   2. The difference between SI and CI on a sum for 3 years at 10% per annum is Rs. 620. Find the principal.
   3. A sum of money amounts to Rs. 12,100 in 2 years under SI and Rs. 12,420 under CI. Find the principal and rate.
   4. A bank offers 10% per annum SI for 2 years and 8% per annum CI for 2 years. Which scheme is better for Rs. 5000?
   5. The CI on a sum for 2 years is Rs. 451.20, while SI for the same period is Rs. 450. Find the rate of interest.

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   IV. Shortcuts and Tricks

   1. CI for 2 years formula: $$CI = P \times \left(\frac{R}{100}\right)^2$$
      
   2. CI for 3 years formula: $$CI = P \times \left(\frac{R}{100}\right)^3 + 3 \times SI$$
      
   3. When CI is compounded half-yearly:
      Use $R/2$ and double the time.
   4. When CI is compounded quarterly:
      Use $R/4$ and multiply time by 4.
   5. CI vs SI for 1 year:
      CI = SI for the first year.