Simple interest

Jenny and Michael are out shopping. Jenny wants an ice cream, but she has run out of money. So she asks Michael if he can lend her some money. If she can borrow enough for an ice cream now, then Michael can get the money back when they return home. Pleeeeeeeeeaaaase?

Hmm. Michael doesn't trust that his sister will pay him back. So he says no. Then Jenny suggests that Michael gets more money back. That he lends enough money for an ice cream now, and then gets all of that money back, plus some extra, when they get back home.

Michael considers the offer, and chooses to take the risk. He pays for Jenny's ice cream. What happened here was that Jenny offered to give Michael interest on the money he loaned to her. Michael loaned Jenny an amount; we can call it the principal. In addition to the principal, Jenny had to repay an additional amount in interest.

Interest is often expressed as a percentage. That's good if you want to compare the interest between different loans. Then we do like this: We take the interest amount, and divide it by the principal. Write it as a percentage, and we have the interest rate. When Jenny bought her ice cream, she borrowed money from Michael with an interest rate of five percent.

She got a loan at five percent interest. Five percent might not sound a lot, but on the other hand she only borrowed the money for a few hours. Now, Jenny might want to borrow for something more costly than an ice cream? She wants to buy a bicycle, a pretty nice one. Michael is willing to lend the money at five percent interest rate.

What amount should he charge her in interest? The principal she needs is equal to the bike's price. Multiply by the interest rate: five per cent. And there you have what Jenny has to pay in interest to borrow for the bicycle. Now, six months have passed and Michael wants his money back.

But Jenny doesn't want to pay him just yet. She wants to continue borrowing the money for another six months. Then, Michael thinks she ought to pay more in interest. Twice the time, that ought to mean twice as much in interest, thinks Michael. Jenny is to pay five percent interest for each six month period that she has borrowed the money.

Five percent in interest after 6 months, and another five after a full year. That's a total of ten percent of the principal. Normally when you talk about interest, you talk about interest per year. When you pay interest several times during the same year, then it often works well to use this simple method of just adding all the interest rates from the year. This simple way of calculating interest is appropriately called: simple interest.