Interest calculation on loans can be a tricky business depending on the type of loan you have. Many of us believe that all loans are calculated based upon the simple interest (SI) formula. This guide will revisit the SI formula and show why it is not used to calculate interest for most loans.
What is the Simple Interest Formula?
The simple interest formula is the base formula for most interest calculations used in finance. Interest is calculated based upon three sets of data: Principal, Rate, and Time. Principal is the amount borrowed, the rate is the percentage of the amount borrowed that is due, and time is the length of time interest is accrued. Putting it all together the simple interest formula is:
I(nterest) = P(rincipal) x R(ate) x T(ime) OR i=P(rt)
What Type of Loan Uses the Simple Interest Formula?
Loans which either pay interest once at maturity or pay interest only on a periodic basis typically use the simple interest formula. Payday and Title loans are the biggest users of this interest calculation method because interest is due at maturity. However, what about personal, student, car, and mortgage loans? These types of loans do not use the simple interest formula, however the interest calculation formulas they do use are based off of the SI formula.
Why Can't the Simple Interest Formula Be Used For My Mortgage or Car Loan?
One reason for why the SI formula is not used for mortgage and car loans is due to a process called amortization. Amortization is basically the paying down of a larger amount over a set period of time. With mortgages, car loans, and similar loans the amount borrowed is payed down over a set period of time. Typically, these pay downs occur monthly with interest paying on the same monthly basis. Since the principal is paid down each month, this means the principal amount changes every month and as a result the interest accrued each month is different.
Another reason the SI formula is not used for mortgages and car loans is because of the use of something called a day count convention. The day count convention is a system by which the number of days is determined between coupon dates or settlement dates and is then used to calculate the interest accrued during this period of time. There are four standard day-count convention methods used to calculate interest:
The two most popular day count conventions used for amortized loans are 30/360 and actual/365. Any financial agreement that results in accrued interest, should state what accrual basis or day count convention is used when calculating interest. If you are not sure that your agreement states this, ask your lender to tell you which day count convention is used for your loan.
How Do I Calculate My Interest Payments Using a Day Count Convention?
Most fixed rate loans either calculate interest using the 30/360 or actual/365 accrual basis. Using a 30/360 accrual basis allows for interest to be calculated based upon a 30 day month regardless if the month has more or less than 30 days in it. These 30 day accrual intervals are accepted to be done within a 360 day calendar year, hence the numerical rendering 30/360. Actual/365 means that each month interest will be calculated based upon the actual days of accrual within a standard 365 day calendar year.
As with the formula for simple interest, interest calculated using different accrual basis or day count conventions follow the base format of Principal x Rate x Time = Interest. The difference is how the aspect of Time is rendered in the formula. Using an accrual basis changes the SI formula into the following:
Interest = (Principal x Rate x Days Accrued) / Number of days in a year
The denominator represents the number of days in a year, and this data is dependent upon what accrual basis the lender is using for your loan. If your lender is using the 30/360 accrual basis then 360 will be in the denominator of the equation. If you calculate your interest on your own, expect to see a margin of error around plus or minus $5.00 due to possible rounding of numbers by the lender.
There are many ways interest can be calculated for financial instruments. Most of these different calculations are derived from the formula for simple interest. However, the simple interest formula itself is only used on very few loan types. While knowing the simple interest formula is a great asset, keep in mind, applying it to your mortgage or auto loan to calculate interest payments will leave you with figures that are vastly different from the schedule your lender provides. Therefore, read your loan agreement or ask your lender exactly how interest is calculated so you can determine if you will be paying the appropriate amount of interest each month for your loan.