## Calculating Interest

Mathematics, Operations (+, -, x, /, etc.), Problem Solving, Fractions

### Objective

Students learn how fractions, decimals, and percents relate to other numbers and concepts.

### Directions

Facts to Know
When money is borrowed, you must pay to use it because someone else is losing an opportunity to use it while you have it. What you pay to use the money is called interest. The rate of interest is a percent. The money you borrow is called the principal. Simple interest is paid only on the principal.
The Interest Formula
To calculate the amount of simple interest on a loan, use this formula:
Interest = Principal x Rate of Interest x Time (or) I = PRT
Rate of Interest
The rate of interest is always given as a percent. You often see rates of interest on loans and investments posted outside of banks.
Time
Time in connection with loans is always expressed in years or parts of a year.
1 month = 1/12 of a year
6 months = 6/12 or 1/2 year
Calculating Interest
To find simple interest, use the formula I = PRT
Sample: How much would a loan of \$500 be at 6% interest for 6 months?
Step 1 Use the interest formula. The formula to calculate interest is this:
Interest = Principal x Rate of Interest x Time (I = P x R x T)
Step 2 Change the rate, given as a percent, to a fraction and reduce. Set up time as a fraction of a year.
R = 6/100 = 3/50
T = 6/12 = 1/2
Step 3 Multiply principal x rate x time. Cancel where possible.
I = 500/1 x 3/50 x 1/2 = \$15
or, after cancelling, I = 5/I x 3/1 x 1/1=\$15
You can also change the percent to a decimal (6% = .06) and the time to a decimal
(6 months = 6/12 = .5) and then multiply.
I = \$500.00 x .06 x .5 = \$15
Sample: A T-shirt costs \$24.99 and a pair of jeans costs \$34.99. Each is on sale for 25% off the original price. If Jenna bought the T-shirt and jeans while they were on sale, what was her total price before adding tax? What is the total amount that Jenna had to pay for her purchase after tax was added? (Tax is 8%.)

`\$24.99 original T-shirt pricex 0.25 discount------\$6.2475 = \$6.25 (rounded to the nearest hundredth)\$24.99-\$6.25------\$18.74 sale price for T-shirt\$34.99 original jeans pricex 0.25 discount------\$8.7475 = \$8.75 (rounded to the nearest hundredth)\$34.99-\$8.75------\$26.24 sale price for jeans`

Jenna paid \$18.74 + \$26.24 = \$44.98 for the T-shirt and jeans.
Discounts and Sales
A discount is used by manufacturers and merchants to mean taking off a certain percentage of the price given in a price list. This price is called the list price. The list price less the discount is known as the net price. The noun "discount" can be used as a verb, too--"We're discounting by 15% the list price on all new cars and trucks during our storewide 'Get into Spring' sale!"
You would ask "What's the discount?" but not, "What's the sale?" Often you have to figure out your own savings during a sale, and this is where understanding decimals and percents comes in handy.
Let's say, for instance, you read that a local amusement park is offering a single, one-day pass to all rides for \$12.50, or a special two-day pass for \$20.00. You do some quick decimal arithmetic.
`\$12.50 one-day passx    2------\$25.00 So your savings on a two day pass is the following: \$25.00 one-day pass-\$20.00 two-day pass-------- \$5.00But, just curious--what percent off is that?\$ 5.00    n                          \$ 5.00   100   500------ = --- --> invert and multiply ------ x --- = ---  or 20% off\$25.00   100                         \$25.00    n    25`

### Resources

• Calculating Simple Interest activity sheet
• Calculating Fractions, Decimals, and Percents activity sheet
• pencils