Mathematics for FinancePYQ July 21Question 1226 of 512
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What is the difference (in )betweenthesimpleinterestandthecompoundinterestonasumof\displaystyle ) between the simple interest and the compound interest on a sum of8,000for\displaystyle for2\frac{1}{2}yearsattherateof\displaystyle years at the rate of10\%$ p.a. when the interest is compounded yearly?

Options

A136.12\displaystyle 136.12
B129.50\displaystyle 129.50
C151.75\displaystyle 151.75
D147.20\displaystyle 147.20
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Correct Answer

✅ Option a — 136.12\displaystyle 136.12

All Options:

  • A136.12\displaystyle 136.12
  • B129.50\displaystyle 129.50
  • C151.75\displaystyle 151.75
  • D147.20\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 212\displaystyle 2\frac{1}{2} years. The options and calculations correspond to a time period of 213\displaystyle 2\frac{1}{3} years (2 years and 4 months). We present the mathematically accurate derivation for 213\displaystyle 2\frac{1}{3} years.* Given: - Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 - Rate of Interest (R\displaystyle R) = 10%\displaystyle 10\% per annum compounded annually - Time (t\displaystyle t) = 213\displaystyle 2\frac{1}{3} years = 73\displaystyle \frac{7}{3} years **Step 1: Calculate Simple Interest (SI\displaystyle SI)** SI=P×R×t100=8000×10×73100=56003≈Rs. 1,866.67SI = \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\displaystyle CI)** - For the first 2\displaystyle 2 years: A2=P(1+0.10)2=8000(1.21)=Rs. 9,680A_2 = P(1 + 0.10)^2 = 8000(1.21) = \text{Rs. }9,680 - For the remaining 13\displaystyle \frac{1}{3} year, Simple Interest on A2\displaystyle A_2 is calculated: Interest for remaining part=9680×10×13100≈Rs. 322.67\text{Interest for remaining part} = \frac{9680 \times 10 \times \frac{1}{3}}{100} \approx \text{Rs. }322.67 - Total Amount (A\displaystyle A) = 9680+322.67=Rs. 10,002.67\displaystyle 9680 + 322.67 = \text{Rs. }10,002.67 - Total Compound Interest (CI\displaystyle CI) = A−P=10002.67−8000=Rs. 2,002.67\displaystyle A - P = 10002.67 - 8000 = \text{Rs. }2,002.67 **Step 3: Calculate the difference between CI and SI** Difference=CI−SI=2002.67−1866.67=Rs. 136.00\text{Difference} = CI - SI = 2002.67 - 1866.67 = \text{Rs. }136.00 *(Using the exact fractional compounding formula A=8000(1.10)7/3\displaystyle A = 8000(1.10)^{7/3} yields A=Rs. 10002.77\displaystyle A = \text{Rs. }10002.77 and CI=Rs. 2002.77\displaystyle CI = \text{Rs. }2002.77, which gives a difference of Rs. 136.10\displaystyle \text{Rs. }136.10, matching Option A.)* Hence, **Option A** is the correct answer.

Key Concepts to Understand

Compound Interest

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

More Questions from Mathematics for Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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