$2$Problem $2$: Amortization

In this problem, we will create a function that counts the number of monthly payments required to pay back a loan

Define a function named count$\_$payments$().$ The function should accept three parameters: amount, rate, and pmt$.$

The parameter amount represents the initial size of a loan that is to be repaid with monthly payments. The parameter

rate is the monthly rate at which the loan collects interest, and pmt is the size of the monthly payment.

The function should calculate and return the number of monthly payments required to repay the loan. This is calculated

by using a loop. Every time the loop executes, the following steps should be performed:

$$ Calculate the new balance. This will be done by multiplying the current balance by $1+$i$,$ and then subtracting

the payment amount. Store the result back into balance, rounded to $2$ decimal places.

$$ Increment a variable used to count the number of payments that have been made.

The loop should continue to run for as long as the balance is greater than zero.

The function should not print anything. It should not create any new lists, and should involve only one loop.