a$.$ A person has an annual income of $20,000,$ of which $2,500$ each

year is invested in a pension fund. The contributions to the fund

are made over $40$ years, and the average rate of return on the fund

is $5\%$ p$.$a$.$ in real terms $($i$.$e$.$ allowing for inflation$).$ The expected life

expectancy at retirement is $20$ years. The real rate of return on

government bonds at the time of retirement is $2\mathrm{.}5\%$ p$.$a$.$ what

annual pension should the person receive?