Mathematics for FinanceMTP June 22Question 1357 of 512
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The difference between simple interest and compound interest on a certain for 2\displaystyle 2 years at 10%\displaystyle 10\% p.a is 10\displaystyle 10. Find the sum.

Options

A1000\displaystyle 1000
B3095\displaystyle 3095
C100\displaystyle 100
D990\displaystyle 990
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Correct Answer

✅ Option a — 1000\displaystyle 1000

All Options:

  • A1000\displaystyle 1000
  • B3095\displaystyle 3095
  • C100\displaystyle 100
  • D990\displaystyle 990

Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Time (t\displaystyle t) = 2\displaystyle 2 years - Rate of Interest (r\displaystyle r) = 10%\displaystyle 10\% per annum - Difference between Compound Interest and Simple Interest (CI−SI\displaystyle CI - SI) = Rs. 10\displaystyle \text{Rs. }10 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2\text{Difference} = P \left(\frac{r}{100}\right)^2 10=P(10100)210 = P \left(\frac{10}{100}\right)^2 10=P(0.10)210 = P (0.10)^2 10=0.01P10 = 0.01 P **Step 2: Solve for P\displaystyle P** P=100.01=Rs. 1,000P = \frac{10}{0.01} = \text{Rs. }1,000 *(Note: The database lists Option C (100\displaystyle 100) as correct, which is a typo in the key. The mathematically correct principal is 1,000, which is 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?

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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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