Math 102 Mathematician: 11.4 Installment Buying ‐ Day 1 When borrowing money, it is often more convenient to repay the loan on a weekly or monthly basis. In other words, borrow money on an plan. Fixed Installment Loan: you pay a amount of money for a set number of payments Example: Open‐end Installment Loan: you pay a amount of money each month Example: FIXED INSTALLMENT LOANS Approach 1 – TABLE Tierra wants to purchase a new sofa for her house at a cost of $800. Macy’s has an advertised finance option of no down payment and 4.5% APR for 24 months. A) The table below gives the finance charge per $100 of the amount financed. Find the total finance charge. B) Use the finance charge to find the total installment price. C) Find the monthly payment. Approach 2 – Formula Tierra wants to purchase a new sofa for her house at a cost of $800. Macy’s has an advertised finance option of no down payment and 4.5% APR for 24 months. Installment Payment Formula m = r 
p 
p = n

m
n t
r = 
r
1  1  
n

n = t = The monthly payment is $ . The amount paid in total is $ . The finance charge is $ . NOTE: You can use either approach – the formula or the table. The only advantage to the formula is that you can actually work backwards and figure out some of the beginning details of the arrangement as long as you know a few details about the payment plan. The Annual Percentage Rate (APR) is often a question asked. Finding APR Jamaal recently purchased a Jaguar XK Coupe for $85,000. He was able to put down $76,000 and took out an installment loan for the remaining money. The installment terms cover 48 monthly payments of $219. A) What finance charge will Jamaal pay? B) What is the APR to the nearest half percent, based upon the following APR table. Number of 7.50% 8.0% 8.50% 9.00% 9.50% Payments 36 11.98 12.81 13.64 14.48 15.32 48 16.06 17.18 18.31 19.45 20.59