IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation
An Indian government index-linked bond pays a real coupon of 2% per annum annually in arrears on a nominal of Rs 100, and is redeemed at par indexed. Indexation uses the index with no lag. The index rose from 200 at issue to 220 at the first coupon date. What is the first coupon payment (in rupees, to two decimal places)?
The first coupon is Rs 2.20, because the real coupon of Rs 2 is scaled by the index ratio 220/200 = 1.10. Leaving out the indexation gives Rs 2.00, and dividing by the ratio gives the wrong figure of Rs 1.82.
- A2.00
- B2.20Correct
- C2.40
- D2.02
- 1.82
Explanation
The coupon is the real coupon rate times nominal times the index ratio. Ratio = 220/200 = 1.10. Coupon = 0.02 × 100 × 1.10 = 2.20. Option 2.00 ignores indexation; 1.82 divides by the ratio instead of multiplying.
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