Mathematics for FinancePYQ Jan 21Question 1220 of 512
All Questions

A sum of money is lent at C.I. rate 20%\displaystyle 20\% p.a. 2\displaystyle 2 years. It would fetch 482\displaystyle 482 more if the interest is compounded half yearly. The sum is:

Options

A19,800\displaystyle 19,800
B19,900\displaystyle 19,900
C20,000\displaystyle 20,000
D20,100\displaystyle 20,100
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 20,000\displaystyle 20,000

All Options:

  • A19,800\displaystyle 19,800
  • B19,900\displaystyle 19,900
  • C20,000\displaystyle 20,000
  • D20,100\displaystyle 20,100

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Rate of Interest (r\displaystyle r) = 20%\displaystyle 20\% per annum - Time (t\displaystyle t) = 2\displaystyle 2 years - Interest difference between compounding half-yearly and annually = Rs. 482\displaystyle \text{Rs. }482 **Step 1: Calculate Compound Interest when compounded annually (CIa\displaystyle CI_a)** Aa=P(1+r)t=P(1+0.20)2=1.44PA_a = P(1 + r)^t = P(1 + 0.20)^2 = 1.44 P CIa=Aa−P=0.44PCI_a = A_a - P = 0.44 P **Step 2: Calculate Compound Interest when compounded half-yearly (CIh\displaystyle CI_h)** - Periodic rate i=20%2=10%=0.10\displaystyle i = \frac{20\%}{2} = 10\% = 0.10 - Number of periods n=2×2=4\displaystyle n = 2 \times 2 = 4 Ah=P(1+i)n=P(1.10)4=1.4641PA_h = P(1 + i)^n = P(1.10)^4 = 1.4641 P CIh=Ah−P=0.4641PCI_h = A_h - P = 0.4641 P **Step 3: Set up the difference equation and solve for P\displaystyle P** CIh−CIa=482CI_h - CI_a = 482 0.4641P−0.44P=4820.4641 P - 0.44 P = 482 0.0241P=4820.0241 P = 482 P=4820.0241=Rs. 20,000P = \frac{482}{0.0241} = \text{Rs. }20,000 Hence, **Option C** is the correct answer.

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free