Mathematics of FinanceMCQMTP June 24 Series IIQuestion 1415 of 512
All Questions

What annual payment will discharge a debt of 770\displaystyle 770 due in 5 years, the rate of interest being 5%\displaystyle 5\% per annum SI ?

Options

A150\displaystyle 150
B140\displaystyle 140
C130\displaystyle 130
DNone of these
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Correct Answer

Option b140\displaystyle 140

All Options:

  • A150\displaystyle 150
  • B140\displaystyle 140
  • C130\displaystyle 130
  • DNone of these

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Detailed Solution & Explanation

Let the annual payment be A\displaystyle A. Under simple interest, the annual payment (installment) required to discharge a debt of D\displaystyle D due in n\displaystyle n years at rate r%\displaystyle r\% p.a. is given by: D=nA+A×r100×n(n1)2D = nA + A \times \frac{r}{100} \times \frac{n(n-1)}{2} Given parameters: * Debt (D\displaystyle D) = Rs. 770\displaystyle \text{Rs. }770 * Time (n\displaystyle n) = 5\displaystyle 5 years * Rate (r\displaystyle r) = 5%\displaystyle 5\% p.a. Substituting the values: 770=5A+A×5100×5(51)2770 = 5A + A \times \frac{5}{100} \times \frac{5(5-1)}{2} 770=5A+A×0.05×202770 = 5A + A \times 0.05 \times \frac{20}{2} 770=5A+A×0.05×10770 = 5A + A \times 0.05 \times 10 770=5A+0.5A770 = 5A + 0.5A 770=5.5A770 = 5.5A Solving for A\displaystyle A: A=7705.5=140A = \frac{770}{5.5} = 140 Thus, the annual payment will be Rs. 140\displaystyle \text{Rs. }140. 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.

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