Mathematics for FinancePYQ Dec 23Question 1558 of 512
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Mr. Sharad got his retirement benefits amounting to 50,00,000\displaystyle 50,00,000. He want to receive a fixed monthly sum of amount for his rest of life, starting after one month and thereafter he want to pass on the same to future generation. He expects to earn an interest of 9%\displaystyle 9\% CI Annually. Determine how much perpetual payment he will receive every month?

Options

A39,500\displaystyle 39,500
B38,500\displaystyle 38,500
C37,500\displaystyle 37,500
D36,600\displaystyle 36,600
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Correct Answer

✅ Option c — 37,500\displaystyle 37,500

All Options:

  • A39,500\displaystyle 39,500
  • B38,500\displaystyle 38,500
  • C37,500\displaystyle 37,500
  • D36,600\displaystyle 36,600

Detailed Solution & Explanation

The present value of a perpetuity is: PV=AiPV = \frac{A}{i} Given: * Retirement benefit (PV\displaystyle PV) = 50,00,000\displaystyle 50,00,000 * Nominal annual rate = 9%\displaystyle 9\% p.a., so periodic monthly rate i=9%12=0.75%=0.0075\displaystyle i = \frac{9\%}{12} = 0.75\% = 0.0075 Substituting the values to find the monthly payment A\displaystyle A: 50,00,000=A0.007550,00,000 = \frac{A}{0.0075} A=50,00,000×0.0075=37,500A = 50,00,000 \times 0.0075 = 37,500 Hence, **Option C** is the correct answer.

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