Problem $6$: Creating an Amortization Schedule

Assume that you have decided to borrow $$160,000$ to purchase a house. Suppose that the loan has a monthly interest rate

of $0\mathrm{.}4\%$ and that you will repay it over a period of $30$ years $(360$ months$).$ According to your results in the previous problem,

you should see that this will result in monthly payments of $$839\mathrm{.}46.$ In this problem, we will use a loop to determine how

much will still be owed on the loan at the end of each year.

Perform the following steps in a single code cell.

$1.$ Create variables named balance, i and pmt to store the initial loan amount, interest rate, and monthly

payment amount mentioned in the paragraph above.

$2.$ Use a loop to perform the following tasks $360$ times. As in Problem $5,$ you will need to use a name other than i

for the loop counter. For convenience, I recommend starting the loop counter at $1$ rather than $0.$

$$ 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.

$$ If current payment marks the end of a year of payments $($i$.$e$.$ if the loop counter is a multiple of $12),$

then print a message in the format shown below. Match the format exactly, including the inclusion of

the period at the end of the sentence. Do not include extra spaces.

The balance at the end of xxxx months will be $xxxx$.$

No lists should be created for this problem, and only one loop should be used.