CA Foundation · Quantitative Aptitude · Mathematics of Finance
Mr. Iyer wants a scheme that pays Rs 6,000 at the end of every year forever, with the first payment one year from today. If the rate of interest is 8% per annum, how much must he invest today?
He must invest Rs 75,000. The present value of an ordinary perpetuity equals the annual payment divided by the interest rate, so 6,000 divided by 0.08 gives 75,000. Adding an immediate payment would apply only if the first payment were due today.
- ARs 48,000
- BRs 72,000
- CRs 75,000Correct
- DRs 81,000
Explanation
For a perpetuity with payments at year end, PV = C / i = 6,000 / 0.08 = Rs 75,000. Rs 81,000 is wrong because it adds the first payment as if it were received today (perpetuity due), and Rs 48,000 multiplies instead of dividing.
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