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Algebra1: Instalment Buying
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Instalment Buying
In the instalment buying scheme a customer is not required to make full payment of the article at the time of buying it but is allowed to pay a part of it at the time of purchase and rest in easy instalments, which could be monthly, quarterly, half yearly or even yearly. The time between two successive instalment dates is called payment period. The instalments are generally paid at the end of the period. Thus, if the instalments are monthly, then first instalment is paid at the end of first month, second at the end of second month and so on. In instalment buying (purchase) scheme the buyer will have to pay more than the actual price of the article, because the seller charges some interest for deferred payments (payments made at later dates).

Understand the following terms:

a. With instalment buying you repay a loan on a monthly basis and you get charged interest. The interest worked into the monthly price is known as a finance charge, which is worked into the monthly price. Here you have the advantage that you get to have the product right away, even though you haven't fully paid for it.
b. The cash price is the amount of the item you want to buy. The amount you finance is the total you borrow. The down payment is the amount of money you pay right away. They are related by the following relationship:
Amount Financed = Cash Price - Down Payment
c. The total instalment price is the total amount you pay i.e. all monthly payments plus down payment.
Total Installment Price = (Monthly payment) x (Number of payments) + Down payment
d. The finance charge is the amount you pay for borrowing the money (the interest paid)
Finance Charge = Total Installment Price - Cash Price
e. The future value of an instalment is the sum of the value of an instalment and interest earned on it at the end of the instalment scheme.
f. The the future value of all instalments: is the sum of the future values of all the instalments at the end of the instalment scheme.
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You'll understand these terms better with the help of following illustration:
Example: The cost of a new car is $15,000. You can make down payment of $300 and finance the rest for $315 per month for 60 months. Find the amount financed, total installment price and finance charge.
Amount Financed = 15,000 - 300 = $12,000
Total Installment Price = (315) 60 + 300 = $18,900
Finance Charge = 18,900 - 15,000 = $3900

The Formula Involved in Borrowing:

A. The interest rate per year is called the Annual Percentage Rage (APR in short form), and lenders are required by law to inform you of the APR on any loan.
B. The formulas A = (1-1 (1+ i )n )x R i and R = Axi (1-1 (1+ i)n ) relate the involved quantities i.e.
              A = amount borrowed
              R = monthly payment
              i = monthly interest rate (APR/12), and
              n = total number of payments
C. You can apply these formulas and use for computing the monthly payment on a given loan, or the amount of money paid as finance charges.

The following example will explain the concept and how to apply it:
Example: If you have a loan of $200 for 18 months at 11.5% APR, compute the finance charge.
              A = 200
              i = 0.115/12 = 0.009583
              n = 18
              R = A x i (1-1 (1+ i ) n ) =200 x 0.009583(1-1 (1+ 0.009583)18 ) = 12.15 per month

Total amount you pay = 12.15 x(18) = 218.70
Finance Charge = 218.70 - 200 = $18.70
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