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.