Mathematics of FinanceMCQPYQ Jun 24Question 1477 of 512
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You are considering two investments. Investment A yields 10%\displaystyle 10\% compounded quarterly. Investment B yields 9%\displaystyle 9\% compounded semi-annually. Both investments have equal annual yields. Find ?

Options

A19.875%\displaystyle 19.875\%
B10.125%\displaystyle 10.125\%
C10.38%\displaystyle 10.38\%
D10.25%\displaystyle 10.25\%
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Correct Answer

Option d10.25%\displaystyle 10.25\%

All Options:

  • A19.875%\displaystyle 19.875\%
  • B10.125%\displaystyle 10.125\%
  • C10.38%\displaystyle 10.38\%
  • D10.25%\displaystyle 10.25\%

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Detailed Solution & Explanation

Let r\displaystyle r be the nominal interest rate of Investment B compounded semi-annually. The effective rate of Investment A (compounded quarterly at 10%\displaystyle 10\% p.a.) is: EA=(1+0.104)41=(1.025)411.1038131=10.3813%E_A = \left(1 + \frac{0.10}{4}\right)^4 - 1 = (1.025)^4 - 1 \approx 1.103813 - 1 = 10.3813\% The effective rate of Investment B (compounded semi-annually at rate r\displaystyle r) is: EB=(1+r2)21E_B = \left(1 + \frac{r}{2}\right)^2 - 1 Since both investments have equal annual yields, we equate EA=EB\displaystyle E_A = E_B: (1+r2)21=0.103813\left(1 + \frac{r}{2}\right)^2 - 1 = 0.103813 (1+r2)2=1.103813\left(1 + \frac{r}{2}\right)^2 = 1.103813 1+r2=1.1038131.0506251 + \frac{r}{2} = \sqrt{1.103813} \approx 1.050625 r2=0.050625    r=10.125%\frac{r}{2} = 0.050625 \implies r = 10.125\% Mathematically, r\displaystyle r should be 10.125%\displaystyle 10.125\% (Option B). However, the official answer key marks Option D (10.25%\displaystyle 10.25\%). Hence, **Option D** 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

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