Mathematics for FinanceMTP Jun 23 Series IQuestion 1518 of 512
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Find the present value of an ordinary annuity of 8\displaystyle 8 quarterly payments of 500\displaystyle 500 each, the rate of interest being 8%\displaystyle 8\% p.a. compounded quarterly

Options

A3270.00\displaystyle 3270.00
B4725.00\displaystyle 4725.00
C3662.50\displaystyle 3662.50
D3266.50\displaystyle 3266.50
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Correct Answer

✅ Option c — 3662.50\displaystyle 3662.50

All Options:

  • A3270.00\displaystyle 3270.00
  • B4725.00\displaystyle 4725.00
  • C3662.50\displaystyle 3662.50
  • D3266.50\displaystyle 3266.50

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of an ordinary annuity compounded quarterly is: PV=A×[1−(1+i)−ni]PV = A \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Quarterly payment (A\displaystyle A) = 500\displaystyle 500 * Number of payments (n\displaystyle n) = 8\displaystyle 8 * Nominal rate = 8%\displaystyle 8\% p.a., so periodic rate i=8%4=2%=0.02\displaystyle i = \frac{8\%}{4} = 2\% = 0.02 Substituting the values: PV=500×[1−(1.02)−80.02]PV = 500 \times \left[ \frac{1 - (1.02)^{-8}}{0.02} \right] Using (1.02)−8≈0.85349\displaystyle (1.02)^{-8} \approx 0.85349: PV=500×[1−0.853490.02]=500×7.32548≈3,662.74PV = 500 \times \left[ \frac{1 - 0.85349}{0.02} \right] = 500 \times 7.32548 \approx 3,662.74 This is closest to Option C (3662.50\displaystyle 3662.50). Hence, **Option C** is the correct answer.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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