At time t = 0 an investor purchased an annuity-certain which paid her £10,000 per annum annually in arrear for three years. The purchase price paid by the investor was £25,000.
The value of the retail price index at various times was as shown in the table below:
Time t (years): t = 0 t = 1 t = 2 t = 3
Retail price index: 170.7 183.3 191.0 200.9
(i) Calculate, to the nearest 0.1%, the following effective rates of return per annum achieved by the investor from her investment in the annuity:
(a) the real rate of return; and
(b) the money rate of return
(ii) By considering the average rate of inflation over the three-year period, explain the relationship between your answers in (a) and (b) of (i).