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

[7]

(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). [2]