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CA Foundation · Quantitative Aptitude · Mathematics of Finance

A perpetuity pays ₹6,000 at the end of each year forever, with the first payment due at the end of year 4 (that is, three full years from now are payment-free). At 10% per annum compound interest, what is its present value today?

The present value is about ₹45,078.89. The perpetuity is worth 6,000 divided by 0.10, which is 60,000, at the end of year 3, one year before the first payment. Discounting this for three years at 10% gives 60,000 divided by 1.331, about 45,078.89.

  1. A₹60,000
  2. B₹45,078.89 approximatelyCorrect
  3. C₹49,586.78 approximately
  4. D₹54,545.45 approximately

Explanation

Value of the perpetuity one year before its first payment (at end of year 3) = 6,000/0.10 = 60,000. Discount this over 3 years: 60,000/(1.1)^3 = 60,000/1.331 = ₹45,078.89. Discounting only 2 years gives 49,586.78, and 1 year gives 54,545.45, which are wrong.

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