Having some knowledge of how to calculate finance charges is always a good thing. Most lenders, as you know, will do this for you, but it can be helpful to be able to check the math yourself. However, it is important to understand that what is presented here is a basic procedure for calculating finance charges, and your lender may be using a more complicated method. There may also be other issues attached with your loan which may affect the charges.
The first thing to understand is that there are two basic parts to a loan. The first issue is called the principal. This is the amount of money that is borrowed. The lender wants to profit from his services (lending you the money), called interest. There are many types of interest, from simple to variable. This article will examine simple interest calculations.
In simple interest deals, the amount of the interest (expressed as a percentage) does not change over the life of the loan. This is often called flat rate or fixed interest.
The simple interest formula is as follows:
Interest = Principal × Rate × time
Interest is the total amount of interest paid.
The principal is the amount lent or borrowed.
Rate is the percentage of the principal charged as interest each year.
To do your math, the rate must be expressed as a decimal, so percentages must be divided by 100. For example, if the rate is 18%, use 18/100 or 0.18 in the formula.
Time is the time in years of the loan.
The simple interest formula is often abbreviated:
I = P X R X T
Simple interest math problems can be used for borrowing or lending. The same formulas are used in both cases.
When money is borrowed, the total amount to be paid back equals the principal borrowed plus the interest charge:
Total repayments = principal + interest
Usually, the money is paid back in regular installments, either monthly or weekly. To calculate the regular payment amount, you divide the total amount to be repaid by the number of months (or weeks) of the loan.
To convert the loan period, ‘T,’ from years to months, you multiply it by 12. To convert ‘T’ to weeks, you multiply by 52 since there are 52 weeks in a year.
Here is an example problem to illustrate how this works.
Example:
A single mother purchases a used car by obtaining a simple interest loan. The car costs $1500, and the interest rate that she is being charged on a loan is 12%. The car loan is to be paid back in weekly installments over two years. Here is how you answer these questions:
- What is the amount of interest paid over the two years?
- What is the total amount to be paid back?
- What is the weekly payment amount?
You were given principal: ‘P’ = $1500, interest rate: ‘R’ = 12% = 0.12, repayment time: ‘T’ = 2 years.
Step 1: Find the amount of interest paid.
Interest: ‘I’ = PRT
= 1500 × 0.12 × 2
= $360
Step 2: Find the total amount to be paid back.
Total repayments = principal + interest
= $1500 + $360
= $1860
Step 3: Calculate the weekly payment amount.
Weekly payment amount = total repayments divided by loan period, T, in weeks. In this case, $1860 divided by 104 weeks equals $17.88 per week.
When the interest is paid weekly, as in the above example, it will reduce the weekly payment as the principal is reduced each week. Using Excel’s payment function, PMT, you will get a weekly payment of $16.20 and not the $17.88 mentioned above. Why is that?
In the first example, the interest is for a single payment, yet the payments are weekly, meaning the interest of $360 is for a single payment at the end of the two years. In the Excel PMT function, the interest is 0.12% divided by 52 weeks, the number of payments in a year, thus reducing the principal with each payment and the total interest to be paid back.
By calculating the payment with Excel and resetting the principal balance weekly, you will not pay $360 in total interest but rather $184.80, nearly half as much in the end. This is why many people will pay their mortgage every two weeks with a “half” payment. It resets the principal every two weeks instead of monthly when it reduces the principal at that time.
Calculating simple finance charges is easy once you have done some practice with the formulas and is especially easy if you can utilize Excel and their preset function formulas. You can also try one of the several online calculators with one at https://www.calculator.net/payment-calculator.html.
For more information on finance charges and loan payments, please contact me directly or seek another fee-only Registered Financial Counselor.
