Mathematics of FinanceMCQMTP Mar 21Question 1314 of 512
All Questions

8,000\displaystyle 8,000 becomes 10,000\displaystyle 10,000 in two years at simple interest. The amount that will become 6,875\displaystyle 6,875 in 3\displaystyle 3 years at the same rate of interest is:

Options

A4850\displaystyle 4850
B5000\displaystyle 5000
C5500\displaystyle 5500
D5275\displaystyle 5275
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b5000\displaystyle 5000

All Options:

  • A4850\displaystyle 4850
  • B5000\displaystyle 5000
  • C5500\displaystyle 5500
  • D5275\displaystyle 5275

Ad

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - First scenario: Principal (P1\displaystyle P_1) = Rs. 8,000\displaystyle \text{Rs. }8,000 becomes Amount (A1\displaystyle A_1) = Rs. 10,000\displaystyle \text{Rs. }10,000 in t1=2\displaystyle t_1 = 2 years under simple interest. - Second scenario: Future Value (A2\displaystyle A_2) = Rs. 6,875\displaystyle \text{Rs. }6,875 in t2=3\displaystyle t_2 = 3 years at the same rate. **Step 1: Calculate the interest rate (R\displaystyle R) from the first scenario** SI1=A1P1=100008000=Rs. 2,000SI_1 = A_1 - P_1 = 10000 - 8000 = \text{Rs. }2,000 SI1=P1×R×t1100SI_1 = \frac{P_1 \times R \times t_1}{100} 2000=8000×R×21002000 = \frac{8000 \times R \times 2}{100} 2000=160R    R=2000160=12.5% per annum2000 = 160 R \implies R = \frac{2000}{160} = 12.5\% \text{ per annum} **Step 2: Calculate the required principal (P2\displaystyle P_2) for the second scenario** A2=P2(1+R×t2100)A_2 = P_2\left(1 + \frac{R \times t_2}{100}\right) 6875=P2(1+12.5×3100)6875 = P_2\left(1 + \frac{12.5 \times 3}{100}\right) 6875=P2(1+0.375)6875 = P_2(1 + 0.375) 6875=1.375P26875 = 1.375 P_2 P2=68751.375=Rs. 5,000P_2 = \frac{6875}{1.375} = \text{Rs. }5,000 Hence, **Option B** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

Related Comparison Tables

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

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

Start Practicing — It's Free