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Learning Slides
Background on Installment Purchase
Some companies will sell you something that costs quite a bit of money and let you make an installment purchase. This kind of purchase lets you pay for the item in several future payments. You get to enjoy the item while you pay for it.
You might see an advertisement for a knife set where you pay just four payments of RM59.95. Installment purchases can be simple like that knife set or they can be more complicated. That all depends on the kinds of terms involved. Some installment purchases will have interest included while others won’t.
Terms
The terms are the conditions of the installment purchase. They tell you what kinds of payments to expect and when you need to pay them. For the knife set, our terms are very simple. All we need to do is to make 4 monthly payments of RM59.95 and we are done. There is no interest mentioned here. These are simple terms.
More complicated terms may have an interest payment involved. They might say that you need to make monthly payments for 5 years and also pay an annual interest of 5%. These more complicated terms are for much larger purchases, such as a car costing you RM20,000.
Formula
Because there is an interest involved in our terms now, our monthly payment won’t be the cost of our car divided by the number of months. We also have to include the interest payment. Good thing for us math learners, we have a formula that allows us to calculate our fixed monthly:
There are two methods to be considered in the interest calculation for installment purchases:
1. Original Balance Method
2. Declining Balance Method - using Constant Ratio Formula
\[ Original\ Balance\ Method\ \\ \\ I = Prt \]
\[ Declining\ Balance\ Method\ \\ \\ I = \frac{Br(n+1)}{2m}\ \ \ \ \ or\ \ \ \ \ r=\frac{2mI}{B(n+1)} \]
Here, P or B stands for the cost of the item or the original balance, r stands for the interest rate, t stands for time in years, m is payment term (i.e., m = 12 for monthly payment or m = 52 for weekly payment or etc.), and n the total number of payments.
Interest charge based on original balance
For an installment purchase, when interest charge is based on the original balance, the simple interest formula is used to calculate interest. Several expressions such as charge based on original unpaid balance charge based on simple interest rate and charge based on flat rate are common used in installment purchases but they all mean the same thing.
Normally, an installment purchase requires a down payment.
\[ \begin{aligned} Original\ balance\ &=\ Cash\ Price\ –\ Down\ Payment \\ B\ &=\ CP\ -\ DP \end{aligned} \]
The total amount paid in an installment plan by the buyer is called installment price; that is,
\[
\begin{aligned}
Installment\ Price\ &=\ Cash\ Price\ +\ Total\ Interest \\
IP\ &=\ CP\ +\ I \\
\end{aligned}
\]
OR
\[ \begin{aligned} Installment\ Price\ &=\ Down\ Payment\ +\ Total\ Monthly\ Payment \\ IP\ &=\ DP\ +\ nR \\ \\ and\\ \\ Monthly\ Payment\ &=\ \frac{Original\ Balance\ +\ Total\ Interest}{number\ of\ payment} \\ R\ &=\ \frac{B\ +\ I}{n} \end{aligned} \]
Example
Let’s use this formula to calculate our monthly payments for our car that costs RM20,000. Note that if n is yearly, then r will be the annual interest rate. If n is monthly, then r will be the monthly interest rate or the annual interest rate divided by 12.
Acknowledgments
Some of the notes above are taken from online course Business 110: Math Class from Study.com
Installment Purchases: Payment & Terms. (2014, December 13). Retrieved from https://study.com/academy/lesson/installment-purchases-payment-terms.html.