Question $1-6$ marks

Timothy is retiring from his job soon at which time his employer will

make the following offer:

A lumpsum amount of $$200,000$

A sum of $$15,000$ at the beginning of each year for the next $25$

years.

If the average interest rate is likely to be $5\mathrm{.}5\%$ p$.$a$.$ for the next

$25$ years, which option should Timothy choose?

Question $2-7$ marks

You are contemplating investing some surplus funds and the following

options are available:

Invest $$50,000$ @ $4\%$ p$.$a$.$ compounded annually for $5$ years.

Invest $$45,000$ @ $3\%$ p$.$a$.$ compounded quarterly for $5$ years.

Invest $$40,000$@$4\mathrm{.}5\%$ p$.$a$.$ compounded semi$-$annually for $5$ years.

Invest $$50,000$@$3\%$ p$.$a$.$ compounded semi$-$annually for $5$ years.

Invest $$55,000$@$0\mathrm{.}5\%$ p$.$a$.$ compounded weekly for $5$ years

Which one of the above is the second$-$best option?

Question $3-10$ marks

You have $20$ years left for your retirement. You wish to accumulate a

sum large enough by that time which will allow you an annual withdrawal

of $$100,000$ every year for $30$ years. The average interest rate between

now and the ${20}^{th}$ year is likely to be $4\%$ p$.$a$.$ From then onwards, for

the next $30$ years, it is likely to be $6\%$ p$.$a$.$

How much should you save in an interest$-$bearing account at the end of

each month to be able to have enough money at the time of retirement

which will allow you your desired withdrawal of $$100,000$ every year

for $30$ years after retirement? Assume that the interest in the

interest$-$bearing account is compounded monthly.