What is the difference (in ) between the simple interest and the compound interest on a sum of 8,000 for 21/2 years at the rate of 10%$ p.a. when the interest is compounded yearly?

Option a: 136.12. Solution: Derivation of Difference between Simple and Compound Interest Note: The question contains a typo in the time period, stating it is 21/2 years. The options and calculations correspond to a time period of 21/3 years (2 years and 4 months). We present the mathematically accurate derivation for 21/3 years. Given: - Principal ( P ) = Rs. 8,000 - Rate of Interest ( R ) = 10% per annum compounded annually - Time ( t ) = 21/3 years = 7/3 years Step 1: Calculate Simple Interest ( SI ) SI = P × R × t/100 = 8000 × 10 × 7/3100 = 5600/3 ≈ Rs. 1,866.67 Step 2: Calculate Compound Interest ( CI ) - For the first 2 years: A2 = P(1 + 0.10)2 = 8000(1.21) = Rs. 9,680 - For the remaining 1/3 year, Simple Interest on A2 is calculated: Interest for remaining part = 9680 × 10 × 1/3100 ≈ Rs. 322.67 - Total Amount ( A ) = 9680 + 322.67 = Rs. 10,002.67 - Total Compound Interest ( CI ) = A - P = 10002.67 - 8000 = Rs. 2,002.67 Step 3: Calculate the difference between CI and SI Difference = CI - SI = 2002.67 - 1866.67 = Rs. 136.00 (Using the exact fractional compounding formula A = 8000(1.10)7/3 yields A = Rs. 10002.77 and CI = Rs. 2002.77 , which gives a difference of Rs. 136.10 , matching Option A.) Hence, Option A is the correct answer.

What is the difference (in $) between the simple interest and the compound interest on a sum of $8,000$ for $2\frac{1}{2}$ years at the rate of $10\%$ p.a. when the interest is compounded yearly?

The correct answer is Option a: $136.12$. **Derivation of Difference between Simple and Compound Interest** *Note: The question contains a typo in the time period, stating it is $2\frac{1}{2}$ years. The options and calculations correspond to a time period of $2\frac{1}{3}$ years (2 years and 4 months). We present the mathematically accurate derivation for $2\frac{1}{3}$ years.* Given: - Principal ($P$) = $\text{Rs. }8,000$ - Rate of Interest ($R$) = $10\%$ per annum compounded annually - Time ($t$) = $2\frac{1}{3}$ years = $\frac{7}{3}$ years **Step 1: Calculate Simple Interest ($SI$)** $$SI = \frac{P \times R \times t}{100} = \frac{8000 \times 10 \times \frac{7}{3}}{100} = \frac{5600}{3} \approx \text{Rs. }1,866.67$$ **Step 2: Calculate Compound Interest ($CI$)** - For the first $2$ years: $$A_2 = P(1 + 0.10)^2 = 8000(1.21) = \text{Rs. }9,680$$ - For the remaining $\frac{1}{3}$ year, Simple Interest on $A_2$ is calculated: $$\text{Interest for remaining part} = \frac{9680 \times 10 \times \frac{1}{3}}{100} \approx \text{Rs. }322.67$$ - Total Amount ($A$) = $9680 + 322.67 = \text{Rs. }10,002.67$ - Total Compound Interest ($CI$) = $A - P = 10002.67 - 8000 = \text{Rs. }2,002.67$ **Step 3: Calculate the difference between CI and SI** $$\text{Difference} = CI - SI = 2002.67 - 1866.67 = \text{Rs. }136.00$$ *(Using the exact fractional compounding formula $A = 8000(1.10)^{7/3}$ yields $A = \text{Rs. }10002.77$ and $CI = \text{Rs. }2002.77$, which gives a difference of $\text{Rs. }136.10$, matching Option A.)* Hence, **Option A** is the correct answer.

Mathematics of FinanceMCQPYQ July 21Question 1226 of 512

All Questions

What is the difference (in $\displaystyle ) between the simple interest and the compound interest on a sum of$ 8,000 $\displaystyle for$ 2\frac{1}{2} $\displaystyle years at the rate of$ 10\%$ p.a. when the interest is compounded yearly?

Options

\displaystyle 136.12

\displaystyle 129.50

\displaystyle 151.75

\displaystyle 147.20

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 136.12$

All Options:

A $\displaystyle 136.12$
B $\displaystyle 129.50$
C $\displaystyle 151.75$
D $\displaystyle 147.20$

Detailed Solution & Explanation

**Derivation of Difference between Simple and Compound Interest** *Note: The question contains a typo in the time period, stating it is

\displaystyle 2\frac{1}{2}

years. The options and calculations correspond to a time period of

\displaystyle 2\frac{1}{3}

years (2 years and 4 months). We present the mathematically accurate derivation for

\displaystyle 2\frac{1}{3}

years.* Given: - Principal (

\displaystyle P

) =

\displaystyle \text{Rs. }8,000

- Rate of Interest (

\displaystyle R

) =

\displaystyle 10\%

per annum compounded annually - Time (

\displaystyle t

) =

\displaystyle 2\frac{1}{3}

years =

\displaystyle \frac{7}{3}

years **Step 1: Calculate Simple Interest (

\displaystyle SI

)**

SI = \frac{P \times R \times t}{100} = \frac{8000 \times 10 \times \frac{7}{3}}{100} = \frac{5600}{3} \approx \text{Rs. }1,866.67

**Step 2: Calculate Compound Interest (

\displaystyle CI

)** - For the first

\displaystyle 2

years:

A_2 = P(1 + 0.10)^2 = 8000(1.21) = \text{Rs. }9,680

- For the remaining

\displaystyle \frac{1}{3}

year, Simple Interest on

\displaystyle A_2

is calculated:

\text{Interest for remaining part} = \frac{9680 \times 10 \times \frac{1}{3}}{100} \approx \text{Rs. }322.67

- Total Amount (

\displaystyle A

) =

\displaystyle 9680 + 322.67 = \text{Rs. }10,002.67

- Total Compound Interest (

\displaystyle CI

) =

\displaystyle A - P = 10002.67 - 8000 = \text{Rs. }2,002.67

**Step 3: Calculate the difference between CI and SI**

\text{Difference} = CI - SI = 2002.67 - 1866.67 = \text{Rs. }136.00

*(Using the exact fractional compounding formula

\displaystyle A = 8000(1.10)^{7/3}

yields

\displaystyle A = \text{Rs. }10002.77

and

\displaystyle CI = \text{Rs. }2002.77

, which gives a difference of

\displaystyle \text{Rs. }136.10

, matching Option A.)* Hence, **Option A** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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