CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest
A firm leases equipment and pays Rs 12,000 at the beginning of each year for 2 years. If the discount rate is 20% p.a., what is the present value of the lease payments (annuity due)?
The present value is Rs 22,000. With payments at the start of each year, the first Rs 12,000 is paid today and is not discounted, while the second is discounted one year at 20% to Rs 10,000. Adding them gives 22,000.
- ARs 22,000Correct
- BRs 18,333
- CRs 24,000
- DRs 26,400
Explanation
For an annuity due, the first payment is at time 0: PV = 12,000 + 12,000/1.2 = 12,000 + 10,000 = Rs 22,000. Rs 18,333 is the ordinary-annuity value (12,000/1.2 + 12,000/1.44). Rs 26,400 is 22,000 x 1.2, which moves the value in the wrong direction. Rs 24,000 ignores discounting.
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