Chapter 3, Problem 5PP

You have just purchased a stereo system that cost $\$1,000$ on the following credit plan: no down payment, an interest rate of 18% per year (and hence 1.5% per month), and monthly payments of $\text{\$50}$ . The monthly payment of $\text{\$50}$ is used to pay the interest, and whatever is left is used to pay part of the remaining debt. Hence, the first month you pay 1.5% of $1,000 in interest. That is $\text{\$15}$ in interest. So, the remaining $\text{\$35}$ is deducted from your debt, which leaves you with a debt of $965.00. The next month, you pay interest of 1.5% of $\text{\$965}\text{.00,}$ which is $\text{\$14}\text{.48}\text{.}$ Hence, you can deduct $\text{\$35}\text{.52}$ (which is $\text{\$50 - \$14}\text{.48}$ ) from the amount you owe. Write a program that tells you how many months it will take you to pay off the loan, as well as the total amount of interest paid over the life of the loan. Use a loop to calculate the amount of interest and the size of the debt after each month. (Your final program need not output the monthly amount of interest paid and remaining debt, but you may want to write a preliminary version of the program that does out put these values.) Use a variable to count the number of loop iterations and hence, the number of months until the debt is zero. You may want to use other variables as well. The last payment may be less than $\text{\$50}$ if the debt is small, but do not forget the interest. If you owe $\text{\$50}$ , your monthly payment of $\text{\$50}$ will not pay off your debt, although it will come close. One month's interest on $\text{\$50}$ is only 75 cents.