13.5 Simple and compound interest


By the end of this section you should be able to: ● understand simple and compound interest ● solve problems involving simple and compound interest


If you have a savings account with a bank and deposit some money, the bank will pay you extra money for saving with them. This is called interest. Similarly, if you need to borrow money from a bank, the bank will expect you to pay back more than you borrowed from them in the fi rst place. How much extra money you pay them back depends on the interest rate set by the bank. Banks and other institutions make their money by charging more interest on their loans compared to the interest they give on their savings accounts.


The following key terms are important for this section: P = Principal


i = Interest rate t = Time F = Final amount The sum of money borrowed or invested over a period of time.


The rate at which interest is paid on a loan or savings. This value is usually represented as a percentage.


The length of time for which the money is borrowed or invested. This value can be expressed in days, weeks, months or years.


The fi nal sum of money due, including interest at the end of the investment or borrowing period.


There are two types of interest rates available: 1. Simple interest 2. Compound interest


Simple interest


Simple interest is calculated by multiplying the principal amount by the interest rate and the duration of a loan or investment. Generally, simple interest paid or received over a certain period is a fi xed percentage of the principal amount that was borrowed or loaned.


Simple interest is interest that is always calculated on the initial principal. Simple interest = principal × rate × time


Worked example 1 A college student obtains a simple interest loan to purchase a car which costs €2 800. The annual interest rate on her loan is 6%. She repaid the entire loan at the end of 3 years. (i) Calculate the interest she paid over the 3 years of her loan. (ii) What was the fi nal amount of the loan?


Solution


When doing calculations, always use the decimal form for interest value.


i = percentage rate


____________ 100


Interest is the sum of money that you pay for borrowing or that is paid to you for investing.


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Linking Thinking 1


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