Question $3$: $[10$ marks$]$ How much must you deposit at the end of each month for $25$ years to fund an

annuity of $$2,500$ per month for $20$ years?

The first annuity withdrawal is made $5$ years after the last deposit and interest changes from $i^{(12)}=8\%$ per

year to $i^{(12)}=7\%$ per year at the time of the first annuity withdrawal.