QUESTION THREE $[20$ MARKS$]$

a$.$ Discuss with at least two supporting points, the main reasons why pension funds are relatively more popular

$(6$ marks$)$

b$.$ A friend has a pension fund of TZS $160$M$.$ The actuarial expectation is that the person will live for another $15$ years. If the $15-$year interest rate $($yield on government bonds$)$ is $9\%$ p$.$a$.,$ how much can be paid to the pensioner at the end of each year?

$(7$ marks$)$

c$.$ Suppose your nephew is planning to retire in $35$ years' time with a pension fund of TZS $190$M$.$ What is the required annual contribution to the Pension fund, if the expected rate of return on the fund is $6\%$ p$.$a$.?$

$(7$ marks$)$