CA Foundation · Quantitative Aptitude · Mathematics of Finance
A perpetuity of ₹5,000 per year is to be paid forever, but the first payment will be made at the beginning of the first year, that is, immediately. At 10% per annum, what is the present value of this perpetuity due?
The present value is ₹55,000. Since the first payment is made immediately, the value is the immediate payment of 5,000 plus the present value of an ordinary perpetuity of 5,000 at 10%, which is 50,000. Together they total 55,000.
- A₹50,000
- B₹55,000Correct
- C₹45,000
- D₹5,000
Explanation
A perpetuity due equals the ordinary perpetuity value plus the immediate first payment. Ordinary perpetuity = 5,000/0.10 = 50,000. Adding the first payment of 5,000 gives ₹55,000. The figure ₹50,000 ignores the immediate payment, which is the key error.
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