Themba Sithole has consulted with you regarding his retirement. He is $45$ years old and he

would like to retire at the age of $65$ years. After a consultation with Mr Sithole the following

was decided:

He would like to receive income after retirement until the age of $90$ years.

His income after retirement must increase annually by a rate of $6\mathrm{.}5\%$ per annum $($the assumed

rate of inflation$).$

After retirement, Mr Sithole would like to receive an income of R$650000$ per annum in

today$$s terms.

He currently contributes R$25000$ per annum to his pension fund and he has no further

retirement provisions. These contributions increase at a rate of $7\mathrm{.}5\%$ per annum and he earns

a $12\%$ return on his investment.

The value of his pension fund is currently R$800000.$

He can earn a return of $15\%($compounded annually$)$ after retirement on the capital invested

at retirement.

Required:

Calculate Themba Sithole$$s retirement gap.