CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
A cooperative society pays Rs 4,000 at the end of every year forever to a charity. If the rate of interest is 8% per annum, what single sum today would fund this perpetuity?
The sum needed is Rs 50,000. The present value of a perpetuity paying at each year end is the annual payment divided by the interest rate, so 4,000 divided by 0.08 equals Rs 50,000. Any other figure misplaces the rate or the decimal.
- ARs 32,000
- BRs 50,000Correct
- CRs 5,000
- DRs 3,20,000
Explanation
Present value of an ordinary perpetuity = payment / rate = 4,000 / 0.08 = Rs 50,000. Rs 32,000 results from multiplying payment by the rate (4,000 x 0.08 = 320 is not it either), so that figure is a wrong base. Rs 5,000 comes from dividing by 0.8 instead of 0.08, a decimal slip.
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