Mathematics for FinanceMTP Jun 23 Series IIQuestion 1387 of 512
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If the compound interest on a certain sum of money for 2\displaystyle 2 years at 5%\displaystyle 5\% p.a. be 50.44\displaystyle 50.44, then the simple interest (S.I.) is

Options

A50\displaystyle 50
B49\displaystyle 49
C48\displaystyle 48
DNone of these
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Correct Answer

✅ Option c — 48\displaystyle 48

All Options:

  • A50\displaystyle 50
  • B49\displaystyle 49
  • C48\displaystyle 48
  • DNone of these

Detailed Solution & Explanation

**Derivation of Simple Interest** Given: - Compound Interest (CI\displaystyle CI) = Rs. 50.44\displaystyle \text{Rs. }50.44 - Time (t\displaystyle t) = 2\displaystyle 2 years - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum **Step 1: Express compound interest in terms of principal P\displaystyle P** CI=P[(1+r)2−1]CI = P \left[ (1 + r)^2 - 1 \right] 50.44=P[(1.05)2−1]50.44 = P \left[ (1.05)^2 - 1 \right] 50.44=P[1.1025−1]50.44 = P [ 1.1025 - 1 ] 50.44=0.1025P50.44 = 0.1025 P P=50.440.1025≈Rs. 492.10P = \frac{50.44}{0.1025} \approx \text{Rs. }492.10 **Step 2: Calculate Simple Interest (SI\displaystyle SI) on the same principal** SI=P×R×t100SI = \frac{P \times R \times t}{100} SI=492.10×5×2100=492.10×0.10≈Rs. 49.21SI = \frac{492.10 \times 5 \times 2}{100} = 492.10 \times 0.10 \approx \text{Rs. }49.21 *(Note: Option B (49\displaystyle 49) is mathematically correct. The database lists Option C (48\displaystyle 48) as correct, which is a typo in the key. We note that 49 is the correct choice.)* Hence, **Option B** 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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