Mathematics for FinancePYQ Nov 20Question 1205 of 512
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On what sum will the compound interest at 5%\displaystyle 5\% per annum for 2\displaystyle 2 years compounded annually be 3,280\displaystyle 3,280?

Options

A32,000\displaystyle 32,000
B16,000\displaystyle 16,000
C48,000\displaystyle 48,000
D64,000\displaystyle 64,000
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Correct Answer

✅ Option a — 32,000\displaystyle 32,000

All Options:

  • A32,000\displaystyle 32,000
  • B16,000\displaystyle 16,000
  • C48,000\displaystyle 48,000
  • D64,000\displaystyle 64,000

Detailed Solution & Explanation

**Derivation of Principal Amount from Compound Interest** Given: - Compound Interest (CI\displaystyle CI) = Rs. 3,280\displaystyle \text{Rs. }3,280 - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum compounded annually - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Set up the Compound Interest equation** CI=P[(1+r100)t−1]CI = P\left[\left(1 + \frac{r}{100}\right)^t - 1\right] 3280=P[(1+0.05)2−1]3280 = P\left[\left(1 + 0.05\right)^2 - 1\right] 3280=P[(1.05)2−1]3280 = P\left[(1.05)^2 - 1\right] 3280=P[1.1025−1]3280 = P[1.1025 - 1] 3280=0.1025P3280 = 0.1025 P **Step 2: Solve for Principal (P\displaystyle P)** \displaystyle ' in math mode at position 44: …ext{Rs. }32,000̲ \text{ (which …" style="color:#cc0000">P = \frac{3280}{0.1025} = \text{Rs. }32,000$ \text{ (which corresponds to 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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