Mathematics of FinanceMCQPYQ Nov. 20Question 1443 of 512
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Which of the following statements is True? (assume that the yearly cash flow? Are identical for both annuities)

Options

AThe present value of annuity due is greater than the present value of an ordinary annuity
BThe present value of an ordinary annuity is greater than the present value of an annuity due
CThe future value of an ordinary annuity is greater than the future value of an annuity due
DThe future value of an annuity due is equal to future value of an ordinary annuity.
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Correct Answer

Option aThe present value of annuity due is greater than the present value of an ordinary annuity

All Options:

  • AThe present value of annuity due is greater than the present value of an ordinary annuity
  • BThe present value of an ordinary annuity is greater than the present value of an annuity due
  • CThe future value of an ordinary annuity is greater than the future value of an annuity due
  • DThe future value of an annuity due is equal to future value of an ordinary annuity.

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Detailed Solution & Explanation

Let's compare the Present Value (PV\displaystyle PV) and Future Value (FV\displaystyle FV) of an Ordinary Annuity and an Annuity Due: 1. For an **Annuity Due**, payments are made at the beginning of each period. Thus, each cash flow is discounted by one less period for PV, and compounds for one more period for FV. 2. The relationships are: PVdue=PVordinary×(1+i)PV_{\text{due}} = PV_{\text{ordinary}} \times (1+i) FVdue=FVordinary×(1+i)FV_{\text{due}} = FV_{\text{ordinary}} \times (1+i) Since (1+i)>1\displaystyle (1+i) > 1 for positive interest rates: * The present value of an annuity due is greater than the present value of an ordinary annuity: PVdue>PVordinary\displaystyle PV_{\text{due}} > PV_{\text{ordinary}}. * The future value of an annuity due is greater than the future value of an ordinary annuity: FVdue>FVordinary\displaystyle FV_{\text{due}} > FV_{\text{ordinary}}. Thus, statement A is the mathematically true statement. (Note: While some answer keys mark C, the correct statement is A). Hence, **Option A** 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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