Question $3$: Retirement planning $15$ marks

The news about the $2-$pot retirement system which kicked$-$off in the country on $1$ September

$2024$ has brought mixed feelings to many people. The system will allocate one$-$third of past

and future retirement contributions to a savings component and the remaining two$-$thirds will

go into a retirement component. In a panicked state, your $35-$year$-$old co$-$worker wants to know

the size of the annual contributions that she must make for the next $25$ years so that she can

retire at age $60.$ She expects to live to an age of $80$ and wants to be able to start making an

annual withdrawal of R$600000$ from the retirement account on her $61$st birthday through to the

$80$th$.$ The account is expected to earn $10\%$ per year for the entire period and the interest will

be compounded monthly.

Required:

$3\mathrm{.}1.$ Calculate the monthly contribution that she must make to the retirement fund over

the next $25$ years. $(6)$

$3\mathrm{.}2.$ Calculate the difference in the monthly contribution if she starts saving only $15$ years

before retirement and her life expectancy after retirement increases to $30$ years. The

return remains unchanged.

$3\mathrm{.}3.$ A retirement planning exercise is useful in that it provides an indication of the level of

investment required, of course, based on certain assumptions. It is however a difficult

exercise in practice. Name two factors that make it such a difficult exercise. $(2)$

$3\mathrm{.}4.$ When compounding occurs, the effective annual interest rate is greater than the

annual percentage rate. Evaluate this statement and substantiate your answer