Mathematics for FinanceMTP Sep 24 Series IIQuestion 3958 of 507
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If the compound interest on a certain sum of money for 2\displaystyle 2 years at 4%\displaystyle 4\% p.a. be 510\displaystyle 510, then its simple interest at same time at same rate of interest is

Options

A500\displaystyle 500
B510\displaystyle 510
C1000\displaystyle 1000
DNone of these
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Correct Answer

✅ Option a — 500\displaystyle 500

All Options:

  • A500\displaystyle 500
  • B510\displaystyle 510
  • C1000\displaystyle 1000
  • DNone of these

Detailed Solution & Explanation

Let the principal be P\displaystyle P. The rate of interest is r=4%\displaystyle r = 4\% p.a., so i=0.04\displaystyle i = 0.04. The time period is t=2\displaystyle t = 2 years. The Compound Interest (CI\displaystyle CI) is given by: CI=P[(1+i)t−1]CI = P\left[(1+i)^t - 1\right] Substituting the values: 510=P[(1.04)2−1]510 = P\left[(1.04)^2 - 1\right] 510=P[1.0816−1]510 = P[1.0816 - 1] 510=0.0816P510 = 0.0816P Solving for P\displaystyle P: P=5100.0816=6,250P = \frac{510}{0.0816} = 6,250 The Simple Interest (SI\displaystyle SI) on the same principal for the same period at the same rate is: SI=P×r×t100SI = \frac{P \times r \times t}{100} SI=6,250×4×2100=500SI = \frac{6,250 \times 4 \times 2}{100} = 500 Thus, the simple interest is Rs. 500\displaystyle \text{Rs. }500. 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

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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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