In the following exercises, find the payment per period necessary to reach a specified future value based on the given interest rate, compounding periods per year, and number of years. Recall, the number of payments per year and the number of compounding periods per year are the same.

Yasmin has analyzed her budget and decides to deposit $$425$ per month in an account bearing $3\mathrm{.}99\%$ interest compounded monthly. How much will be in the account after $20$ years? After $30$ years? After $40$ years?