A worker aged 35 wishes to accumulate a fund for retirement by depositing $1, 000 at the beginning of each month for 30 years. Starting at age 65 the worker plans to make 15 annual withdrawals at the beginning of each year. Assume that all payments are certain to be made. If the annual effective rate of interest is 6% during the first 30 years but only 4% thereafter,

find:

(a) the value of the fund at age 65.

(b) the amount of each withdrawal starting at age 65.

(c) how much total interest will s/he earn throughout the 45-year span? [2 marks]