CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
A scholarship pays Rs 5,000 at the beginning of every year forever, the first payment being made today. If the rate of interest is 10% per annum, what is the present value of this perpetuity due?
The present value is Rs 55,000. The first Rs 5,000 is paid immediately, and the remaining payments form an ordinary perpetuity worth 5,000 divided by 0.10, which is Rs 50,000. Adding the two gives Rs 55,000, higher than the ordinary perpetuity value.
- ARs 50,000
- BRs 45,000
- CRs 55,000Correct
- DRs 5,500
Explanation
Perpetuity due = payment + payment/rate = 5,000 + 5,000/0.10 = 5,000 + 50,000 = Rs 55,000. Rs 50,000 is the ordinary perpetuity value, ignoring that the first payment is made today. Rs 45,000 subtracts instead of adds the first payment.
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