Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually.

₹2,100. A = 10000(1.1)^2 = 12,100, so CI = 12100 - 10000 = ₹2,100.

The difference between the compound interest and the simple interest on a sum for 2 years at 10% per annum is ₹50. What is the sum?

₹5,000. For 2 years, CI - SI = P ( R100 )^2 = 0.01P = 50, so P = ₹5,000.

A sum becomes ₹1,323 in 2 years at 5% per annum compound interest. What is the sum?

₹1,200. P = 1323(1.05)^2 = 13231.1025 = ₹1,200.

Find the amount on ₹8,000 for 1 year at 10% per annum, compounded half-yearly.

₹8,820. Half-yearly compounding uses a rate of 5\% per period for 2 periods: A = 8000(1.05)^2 = ₹8,820.

A sum amounts to ₹6,050 in 2 years and to ₹6,655 in 3 years at compound interest. What is the annual rate of interest?

10%. The amount grows by the same factor each year, so the rate is 6655 - 60506050 100 = 10\%.

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Quantitative Aptitude · Commercial Maths

Compound Interest — Questions & Answers

Compound interest is charged on the running amount, so it grows geometrically. Adjust the rate and the number of periods when compounding is more frequent than yearly.

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$A = P\left(1 + \dfrac{R}{100}\right)^T$ ; $\;CI = A - P$
Half-yearly: rate $\dfrac{R}{2}$ per period, $2T$ periods. Quarterly: $\dfrac{R}{4}$ , $4T$ periods
For 2 years, $CI - SI = P\left(\dfrac{R}{100}\right)^2$

5 solved Compound Interest questions

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01
Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually.
4 steps · reveal one at a time
1. Step 1: Recall the formula
  To find the Amount ( $A$ ) when interest is compounded annually, we use the formula $A = P(1 + R/100)^n$ . Here, $P$ is the principal, $R$ is the rate of interest, and $n$ is the number of years.
2. Step 2: Calculate the amount
  Substitute the given values into the formula: $P = 10,000$ , $R = 10\%$ , and $n = 2$ years. So, $A = 10000(1 + 10/100)^2 = 10000(1.1)^2$ . This calculation gives us $A = 10000 \times 1.21 = 12100$ .
3. Step 3: Find the interest
  The Compound Interest ( $CI$ ) is the difference between the final amount and the initial principal. So, $CI = A - P = 12100 - 10000$ . This gives us a compound interest of $\text{Rs}\,2,100$ .
4. Step 4: The answer
  So the answer is (B) ₹2,100. This is the total interest earned on ₹10,000 over two years at 10% compounded annually.
02
The difference between the compound interest and the simple interest on a sum for 2 years at 10% per annum is ₹50. What is the sum?
5 steps · reveal one at a time
1. Step 1: Understand the Problem
  We need to find the principal sum (P) given that the difference between the compound interest (CI) and simple interest (SI) for 2 years at a rate (R) of 10% per annum is ₹50.
2. Step 2: Recall the Formula
  For a period of 2 years, there's a direct formula for the difference between CI and SI. It is given by $CI - SI = P\left(\dfrac{R}{100}\right)^2$ .
3. Step 3: Apply the Formula
  Substitute the given values into the formula: $50 = P\left(\dfrac{10}{100}\right)^2$ . This simplifies to $50 = P\left(\dfrac{1}{10}\right)^2$ , which further becomes $50 = P\left(\dfrac{1}{100}\right)$ .
4. Step 4: Calculate the Sum
  Now, we can easily solve for P. From $50 = P\left(\dfrac{1}{100}\right)$ , we multiply both sides by 100 to get $P = 50 \times 100$ . This gives us $P = \text{Rs}\,5,000$ .
5. Step 5: The answer
  So the answer is (A) ₹5,000. This is the principal sum for which the difference between CI and SI is ₹50 under the given conditions.
03
A sum becomes ₹1,323 in 2 years at 5% per annum compound interest. What is the sum?
5 steps · reveal one at a time
1. Step 1: Identify Given Values
  We are given the final amount ( $A = \text{Rs}\,1,323$ ), the time period ( $n = 2$ years), and the compound interest rate ( $r = 5\%$ per annum). We need to find the initial principal sum ( $P$ ). Convert the rate to decimal: $r = 0.05$ .
2. Step 2: Recall Compound Interest Formula
  The formula for the amount ( $A$ ) after $n$ years with compound interest is $A = P(1 + r)^n$ , where $P$ is the principal and $r$ is the annual interest rate. To find $P$ , we can rearrange the formula to $P = \dfrac{A}{(1 + r)^n}$ .
3. Step 3: Substitute and Calculate
  Now, substitute the given values into the rearranged formula: $P = \dfrac{1323}{(1 + 0.05)^2}$ . This simplifies to $P = \dfrac{1323}{(1.05)^2}$ . Calculate the denominator: $(1.05)^2 = 1.1025$ . So, $P = \dfrac{1323}{1.1025}$ .
4. Step 4: Perform Final Division
  Divide the amount by the calculated factor: $P = \dfrac{1323}{1.1025} = 1200$ . Therefore, the initial sum is ₹1,200.
5. Step 5: The answer
  So the answer is (B) ₹1,200, as this is the principal sum we calculated using the compound interest formula.
04
Find the amount on ₹8,000 for 1 year at 10% per annum, compounded half-yearly.
4 steps · reveal one at a time
1. Step 1: Understand Compounding
  The question asks for the amount when interest is compounded half-yearly for 1 year. This means the interest will be calculated twice within the year.
2. Step 2: Adjust Rate and Periods
  The annual rate is $10\%$ . For half-yearly compounding, the rate per period is $10\% \div 2 = 5\%$ . For 1 year, there are $1 \times 2 = 2$ compounding periods.
3. Step 3: Calculate Final Amount
  We use the compound interest formula $A = P(1 + r)^n$ . Here, $P = \text{\text{Rs}\,}8,000$ , $r = 0.05$ (for $5\%$ ), and $n = 2$ . So, $A = 8000(1 + 0.05)^2 = 8000(1.05)^2$ .
4. Step 4: The answer
  So the answer is (D) ₹8,820. Calculating $8000 \times (1.05)^2 = 8000 \times 1.1025 = \text{\text{Rs}\,}8,820$ . This is the final amount.
05
A sum amounts to ₹6,050 in 2 years and to ₹6,655 in 3 years at compound interest. What is the annual rate of interest?
4 steps · reveal one at a time
1. Step 1: Understand Compound Growth
  With compound interest, the amount grows by a consistent factor each year. This means the interest earned in any given year is calculated on the total amount from the previous year, not just the initial principal.
2. Step 2: Find One-Year Interest
  We know the amount after 2 years is $\text{Rs}\,6,050$ and after 3 years is $\text{Rs}\,6,655$ . The difference between these two amounts is the interest earned in the third year. This is $\text{Rs}\,6,655 - \text{Rs}\,6,050 = \text{Rs}\,605$ .
3. Step 3: Calculate the Rate
  The interest of $\text{Rs}\,605$ was earned on the amount at the end of the second year, which was $\text{Rs}\,6,050$ . To find the annual rate, we divide the interest by this amount and multiply by 100: $\frac{605}{6050} \times 100 = 10\%$ .
4. Step 4: The answer
  So the answer is (C) 10%. The annual rate of interest is $10\%$ , as the amount increased by $10\%$ from the second year to the third year.

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