CA Foundation · Quantitative Aptitude · Mathematics of Finance
A perpetuity pays ₹5,000 at the end of every year, with the first payment at the end of year 4 (no payments before that). At 10% per annum, what is its present value today?
The present value is about ₹37,566. The perpetuity is worth ₹5,000/0.10 = ₹50,000 at the end of year 3, one year before the first payment, and this must be discounted three years at 10%, giving ₹50,000/1.331.
- A₹50,000
- B₹37,566Correct
- C₹41,322
- D₹34,151
Explanation
Value one year before the first payment (at end of year 3) = 5,000/0.10 = 50,000. Discount 3 years: 50,000/1.331 = ₹37,566 (approx). Option ₹50,000 ignores deferment; ₹41,322 discounts only 2 years (50,000/1.21); ₹34,151 discounts 4 years.
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