While many simulations involve randomness, many others are deterministic. We saw an example of this in class $($the braking simulation$).$ As we learn the basics of discrete time$-$based simulation, we will consider another simple deterministic scenario.

Here, we want to build a tool to compare the financial implications of different forms of debt. People are often familiar with the idea that credit card debt is very costly$,$ but don$$t understand the impacts of various interest rates and re$-$payment plans.

Consider a debt of $$10,000.$ Your program should take as input a monthly payment amount, and an interest rate. The interest rate should be accepted as a decimal, not a percentage.

Your tool should then calculate the outstanding debt each month, for a time frame of $60$ months. For each month, the outstanding debt at the end of the month is the amount owing at the beginning of the month $($i$.$e$.,$ the end of the previous month$),$ less the amount of the monthly payment, plus the amount of the interest. The monthly rate of interest is the annual rate divided by $12.$

For example, if the amount owing at the start of the month was $$10,000,$ the monthly payment was $$1,000,$ and the annual interest rate was $12\%,$ then:

The monthly interest rate is $0\mathrm{.}12/12=0\mathrm{.}01$;

After the payment, the amount owing is $$10,000-$ $$1,000=$ $$9,000$;

The amount of new interest is $$9,000*0\mathrm{.}01=$ $$90$

The total owing at the end of the month is $$9,000+$ $$90=$ $$9,090.$

Your main simulation function should start with a balance of $$10,000$ owing, and take the amount of the monthly payment and the interest rate as arguments. It should then print out a list showing, for each month, the amount owing.