The following terms of payment for an annuity are as follows: Periodic payment $=$ P$20,000$

Payment interval $=1$ month

Interest rate $=18\%$ compounded monthly Terms $=15$ years

$1.$ Find the present worth paid of all the payments if it is paid at the end of each month.

$2.$ Find the difference between the sums of an annuity due and an ordinary annuity on these payments.

$3.$ Find the difference between the present values of an annuity due and an ordinary annuity based on these payments.

Ans. $1.$ P$1,214,911\mathrm{.}2462.$ P$271,687\mathrm{.}353.$ P$18,628\mathrm{.}67$