Mathematics of FinancePYQ Jan 26Question 4208 of 507
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An investor intends to purchase a three years bond at a price of ₹ 907.125 having nominal interest rate of 10%. What is the par value of the bond if it matures at par and the investor requires returns at the rate of 14%?

Options

A₹ 1,200
B₹ 1,100
C₹ 900
D₹ 1,000
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Correct Answer

Option d₹ 1,000

All Options:

  • A₹ 1,200
  • B₹ 1,100
  • C₹ 900
  • D₹ 1,000

Detailed Solution & Explanation

The value of a bond is calculated as the sum of the present values of its annual coupon payments and its redemption (par) value at maturity.

Let F\displaystyle F be the par value of the bond.
- Nominal coupon rate = 10%\displaystyle 10\% of par value, so the annual coupon payment is C=0.10F\displaystyle C = 0.10F.
- Life of the bond (n\displaystyle n) = 3\displaystyle 3 years.
- Required rate of return (y\displaystyle y) = 14%=0.14\displaystyle 14\% = 0.14.
- Purchase price (V\displaystyle V) = ₹ 907.125\displaystyle 907.125.

The valuation formula is:
V=C×[1(1+y)ny]+F×(1+y)nV = C \times \left[ \frac{1 - (1+y)^{-n}}{y} \right] + F \times (1+y)^{-n}
Substitute the given values:
907.125=(0.10F)×[1(1.14)30.14]+F×(1.14)3907.125 = (0.10F) \times \left[ \frac{1 - (1.14)^{-3}}{0.14} \right] + F \times (1.14)^{-3}

Let us calculate the discount factors:
(1.14)3=11.4815440.67497(1.14)^{-3} = \frac{1}{1.481544} \approx 0.67497
1(1.14)30.1410.674970.14=0.325030.142.32164\frac{1 - (1.14)^{-3}}{0.14} \approx \frac{1 - 0.67497}{0.14} = \frac{0.32503}{0.14} \approx 2.32164

Substitute these values back into the equation:
907.125=(0.10F)×(2.32164)+F×(0.67497)907.125 = (0.10F) \times (2.32164) + F \times (0.67497)
907.125=F×(0.232164+0.67497)907.125 = F \times (0.232164 + 0.67497)
907.125=F×(0.907134)907.125 = F \times (0.907134)F=907.1250.9071341,000F = \frac{907.125}{0.907134} \approx 1,000
Thus, the par value of the bond is ₹ 1,000.

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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