Slide 1Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Percent and Problem Solving:

Interest

Section 7.6

Slide 2Copyright © 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 3Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Simple Interest

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 4Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Find the simple interest after 2 years on $500 at an interest rate of 12%.

Slide 5Copyright © 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 6Copyright © 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 7Copyright © 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 8Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Calculating Compound Interest

Term Definition

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 9Copyright © 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.

1n t

rA P

n

Slide 10Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

$1800 is invested at 2% interest compounded annually. Find the total amount after 3 years.

Slide 11Copyright © 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)