Simple Interest

I. Intro to Interest

Interest (I) is the fee paid by a borrower to a lender for using the lender’s money. As a borrower, the interest paid is an expense. But as a lender or an investor, interest earned is income. 

There are two basic types of interest:

1) Simple interest: This type of interest is computed on the principal — the amount borrowed — for the entire length of time of the transaction.

2) Compound interest: This interest builds on itself. Money earned in interest for part of the time period is reinvested and used in the computation of interest for the rest of the time period.

II. Simple Interest

The formula for computing the amount of simple interest earned on a particular amount of money is

I = Prt

where:

Interest (I) - Is the amount of interest

Principal (P) - The present value of the principal. The amount of money that you lend or borrow

Rate of Interest (r) - The rate of interest that is charged usually expressed as an annual percentage. The percentage of the principal that it costs to borrow the money

Time (t) - The length of the loan which can range between days, months or years.  

To compute, you simply fill in the variables you have numbers for and solve for the missing ones.

Example

Suppose Jake borrows $4,000 for a new piece of equipment. He borrows the money for 2 years at 11.5% interest. How much does he pay in interest, and what’s the total amount he has to repay? 

To solve this problem, simply plug your numbers into the formula (I = Prt), like this: $4,000(11.5%)(2 years) = $4,000(0.115)(2) = $920. So Jake owes $920 in interest plus what he borrowed, which is $920 + $4,000 = $4,920.

Simple interest is frequently used when small businesses act as lenders in order to sell products.

Example

Delores purchases a new bedroom set from a local furniture store. She makes arrangements with the
store to pay for the $3,995 bedroom set over the next 4 years at 12% interest (simple interest). If she is to make equal monthly payments, how much are those payments?

First determine the amount of interest that she’s paying by using I = Prt: $3,995(0.12)(4) = $1,917.60. 

Add the interest to the cost of the bedroom set to get the total amount: $3,995 + $1,917.60 = $5,912.60.

Now divide the total amount by 48 (4 years × 12 months per year) to get $5,912.60 ÷ 48 = $123.17916

The division doesn’t come out evenly, so Delores will pay $123.18 each month for the first 47 months, and then she’ll pay $123.14 for her last payment. How did I figure the last payment? Well, if you multiply $123.18 by 47, you get $5,789.46 in payments. That leaves $5,912.60 – $5,789.46 = $123.14 for the 48th payment

Example (less than a year)

Julio borrowed $1,100 from Maria five months ago. When he first borrowed the money, they agreed that he would pay Maria 5% simple interest. If Julio pays her back today, how much interest does he owe her?

P = $1,100

r = 5% (per year)

t = 5 months

The interest rate is an annual rate, so to use the simple interest formula you have to express time as 5/12.

I = $1,100 x 0.05 x 5/12

I = $22.92

Solving For Different Values

The simple interest formula can be rearranged to solve for other variables as well.

Principal: P = I/rt

Interest rate: r = I/Pt

Time: t = I/Pr

Reference:

Business/Technical Mathematics:Simple Interest

Business And Financial Mathematics

Business Math for Dummies