Chapter 4, Problem 10P

The balance of a loan, B, after n monthly payments is given by

$B=A{\left(1+\frac{r}{1200}\right)}^n-\frac{P}{r/1200}\left[{\left(1+\frac{r}{1200}\right)}^n-1\right]$

where A is the loan amount, P is the amount of a monthly payment, and r is the yearly interest rate entered in % (e.g., 7.5% entered as 7.5). Consider a 5-year, $20,000 car loan with 6.5% yearly interest that has a monthly payment of $391.32. Calculate the balance of the loan after every 6 months (i.e., at n = 6, 12, 18, 24 ... 54, 60). Each time, calculate the percent of the loan that is already paid. Display the results in a three-column table, where the first column displays the month and the second and third columns display the corresponding value of B and percentage of the loan that is already paid, respectively.