Chapter 2.1, Problem 18E

An Amortization Table Suppose you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the loan in t months. Then your monthly payment can be calculated using

$M=\frac{\mathrm{Pr}{\left(1+r\right)}^t}{{\left(1+r\right)}^t-1}$ dollars.

Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $3500 at a 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.

a. What is your monthly payment?

b. Let’s look ahead to the time when the loan is paid off.

i. What is the total amount you paid to the bank?

ii. How much of that was interest?

c. The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by

$B=P\times \left(\frac{{\left(1+r\right)}^t-{\left(1+r\right)}^k}{{\left(1+r\right)}^t-1}\right)$ dollars.

i. How much do you still owe the bank after 1 year of payments?

ii. An amortization table is a table that shows how much you still owe the bank after each payment. Make an amortization table for this loan.