CA Foundation · Quantitative Aptitude · Mathematics of Finance
A charitable trust wants to fund an annual prize of ₹12,000 paid at the beginning of every year forever, with the first prize paid today. If the rate of interest is 8% per annum, what amount must the trust set aside today?
The trust must set aside ₹1,62,000. When the first prize is paid today, the perpetuity is an annuity-due: present value equals the immediate payment of ₹12,000 plus the ordinary perpetuity value ₹12,000/0.08 = ₹1,50,000.
- A₹1,50,000
- B₹1,62,000Correct
- C₹1,38,000
- D₹1,44,000
Explanation
For a perpetuity-due, PV = payment + payment/i = 12,000 + 12,000/0.08 = 12,000 + 1,50,000 = ₹1,62,000. The option ₹1,50,000 treats it as an ordinary perpetuity (first payment after one year), which ignores the payment made today.
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