Slide 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Percent and Problem Solving: Interest Section7.6

Slide 2 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Calculating Simple Interest Interest is the money charged for using other people’s money. When you borrow money, you pay interest. When you loan or invest money, you earn interest. The money borrowed, loaned, or invested is called the principal amount, or simply principal. Interest is normally stated in terms of a percent of the principal for a given period of time. The interest rate is the percent used in computing the interest. When interest is computed on the original principal, it is called simple interest.

Slide 3 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Simple Interest Simple Interest = Principal · Rate · Time I = P · R · T where the rate is understood to be per year and time is in years.

Slide 4 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Find the simple interest after 2 years on $500 at an interest rate of 12%.

Slide 5 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example A student borrowed $1500 for 9 months on her credit card at a simple interest rate of 20%. How much interest did she pay?

Slide 6 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Total Amount Finding the Total Amount of a Loan or Investment total amount (paid or received) = principal + interest

Slide 7 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example A company borrows $62,500 for 2 years at a simple interest of 12.5% to buy an airplane. Find the total amount paid on the loan.

Slide 8 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Calculating Compound Interest TermDefinition Compound Interest Computed on not only the principal, but also on the interest already earned in previous compounding periods. Compounded Annually Interest is added to the principal at the end of each year and that next year’s interest is computed on this new amount.

Slide 9 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Compound Interest Compound Interest Formula The total amount A in an account is given by where P is the principal, r is the interest rate written as a decimal, t is the length of time in years, and n is the number of times compounded per year.

Slide 10 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example $1800 is invested at 2% interest compounded annually. Find the total amount after 3 years.

Slide 11 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example $5500 is invested at 6.25% interest compounded daily. Find the total amount after 5 years. (1 year = 365 days)