IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation
An investment earns a nominal effective annual return of 8% while the price index rises by 5% each year. What is the real effective annual rate of return, to two decimal places?
The real rate of return is 2.86%. It comes from dividing one plus the nominal rate by one plus the inflation rate, 1.08/1.05, and subtracting one. Simply subtracting 5% from 8% to get 3% ignores compounding and overstates the real return.
- A2.86%Correct
- B3.00%
- C2.76%
- D13.40%
- 2.50%
Explanation
The real rate satisfies (1+i) = (1+r)(1+e), so r = 1.08/1.05 - 1 = 0.028571, or 2.86%. The simple difference 8% - 5% = 3.00% ignores the compounding interaction between interest and inflation, so it is wrong.
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
- An Indian investor earns a money rate of interest of 9% per annum effective, while inflation is 5% per annum. What is the real rate of inter…
- An investor in Pune earns a money effective annual return of 9.18% while inflation runs at 3% per year. What is the real effective annual ra…
- 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…
- An investor buys an index-linked bond whose payments are linked to an index with no lag. Which statement about the real yield is correct if …
- 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 …
- Inflation is expected to be 6% per annum effective, and a bond provides a real yield of 2% per annum effective. What money effective annual …