CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
Mr. Iyer buys a security that pays Rs 6,000 at the end of every year forever. If the required rate of return is 8% per annum, what is the present value of this perpetuity?
The present value is Rs 75,000. A perpetuity paid at the end of each year is worth the annual payment divided by the interest rate, so 6,000 divided by 0.08 gives 75,000. Multiplying by 1.08 would wrongly treat it as a perpetuity due.
- ARs 75,000Correct
- BRs 81,000
- CRs 480
- DRs 7,50,000
Explanation
For an ordinary perpetuity, PV = payment / rate = 6,000 / 0.08 = Rs 75,000. Rs 81,000 is 75,000 x 1.08, which wrongly treats the first payment as due now. Rs 480 multiplies instead of dividing, and Rs 7,50,000 divides by 0.008, a decimal slip.
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