IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation
An annuity pays Rs 20,000 at the end of the first year, with payments increasing each year by the rate of inflation, 5% per annum, for 10 years. Money interest is 10.25% effective per annum. What is the present value, to the nearest rupee?
The real rate is 5%, so each payment's present value is 20,000 x 1.05^-(t+1). The total is 20,000/1.05 x a10 at 5%, i.e. 19,047.62 x 7.7217, about Rs 1,47,080. This differs from every listed option.
- ARs 1,54,217Correct
- BRs 1,45,450
- CRs 1,62,111
- DRs 1,60,000
- Rs 2,00,000
Explanation
Real rate = 1.1025/1.05 - 1 = 5%. PV = (20,000/1.05) a(10) at 5% ... payments grow at 5% and discount at 10.25%, so PV = 20,000 x v-sum with each term 1.05^(t-1)/1.1025^t = (1/1.05)... 1.05^(t-1)/1.05^(2t) = 1.05^(-t-1). PV = 20,000/1.05 x a10 at 5% = 19,047.62 x 7.72173 = 1,47,080.
Did you get it right without looking?
One question tells you little. A timed set on Allowing for inflation shows your real accuracy, how long you take and where you lose marks.
More Allowing for inflation questions
- A price index rises by 4% in the first year, 6% in the second year and 5% in the third year. What is the equivalent constant annual rate of …
- An investor in Pune requires a real effective annual return of 3% when inflation is expected to run at 6% per annum. What money effective an…
- A conventional 1-year zero-coupon bond yields 8.00% per annum effective, while a 1-year zero-coupon index-linked bond with no indexation lag…
- The price index for a basket of goods was 240 at the start of 2022 and 264 at the start of 2023. What was the annual rate of inflation over …
- A price index was 200 at the start of year 1, and annual inflation was 5% in year 1 and 8% in year 2. What is the index at the end of year 2…
- If the real rate of interest is 3% per annum and inflation is 5% per annum, which of the following is the money rate of interest per annum?