Mathematics of FinancePYQ May 25Question 4015 of 507
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Raju will pay instalments of ₹ 3,150 per month for the next 3 years towards his loan at an interest rate 12.4%, discounted monthly, what was the approximate amount of loan taken initially?[Given that (1.01033)36=1.448\displaystyle (1.01033)^{36} = 1.448]

Options

A₹ 13,683.60
B₹ 9,742.29
C₹ 94,345.17
D₹ 74,158.24
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Correct Answer

Option c₹ 94,345.17

All Options:

  • A₹ 13,683.60
  • B₹ 9,742.29
  • C₹ 94,345.17
  • D₹ 74,158.24

Detailed Solution & Explanation

This is a loan repayment problem, which corresponds to the present value of an ordinary annuity since installments are paid at the end of each period.
Given details:
- Monthly installment (A\displaystyle A) = 3,150\displaystyle ₹ 3,150
- Nominal annual interest rate (r\displaystyle r) = 12.4%=0.124\displaystyle 12.4\% = 0.124
- Number of years (t\displaystyle t) = 3\displaystyle 3

The interest rate is compounded monthly, so the monthly interest rate (i\displaystyle i) is:
i=0.124120.0103333i = \frac{0.124}{12} \approx 0.0103333
In this problem, the given base value uses i=0.01033\displaystyle i = 0.01033:
i=0.01033i = 0.01033
The total number of monthly payments (n\displaystyle n) over 3\displaystyle 3 years is:
n=3×12=36n = 3 \times 12 = 36
The formula for the present value of an ordinary annuity (PV\displaystyle PV) is:
PV=A×[1(1+i)ni]PV = A \times \left[\frac{1 - (1 + i)^{-n}}{i}\right]
Substitute the given values into the formula:
PV=3150×[1(1.01033)360.01033]PV = 3150 \times \left[\frac{1 - (1.01033)^{-36}}{0.01033}\right]
We are given that (1.01033)36=1.448\displaystyle (1.01033)^{36} = 1.448. Therefore:
(1.01033)36=11.4480.6906077(1.01033)^{-36} = \frac{1}{1.448} \approx 0.6906077
Now substitute this back:
PV=3150×[10.69060770.01033]PV = 3150 \times \left[\frac{1 - 0.6906077}{0.01033}\right]PV=3150×[0.30939230.01033]PV = 3150 \times \left[\frac{0.3093923}{0.01033}\right]
PV=3150×29.95085=94345.18PV = 3150 \times 29.95085 = 94345.18
So the initial loan amount taken was approximately 94,345.17\displaystyle ₹ 94,345.17.
Hence, **Option C** 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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