Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
6. Simple Interest
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Exercise 31 Page 270

Use the simple interest formula to find the interest.

$ 8500

Practice makes perfect

Let's start by looking at the second row of the given table!

Principal Annual Interest Rate Time Simple Interest
$12 000 4.25 % 5 years $2550
6.5 % 18 months $828.75
We want to calculate the principal. We can do so using the simple interest formula that tells us that the simple interest I is the product of the principal P, annual interest rate (in decimal form) r, and time (in years) t. I=Prt Here, the simple interest I is 828.75 dollars and the time t is 18 months. First, we can convert the time t from months to years. We can do using the conversion factor 1year12months.
18months * 1year/12months
18months * 1years/12months
â–Ľ
Simplify quotient
18months * 1year/12months
18* 1year/12
18year/12
18/12 year
1.5 year
The time t is equal to 1.5 year. We also know that the interest rate of 6.5 % can be written as 0.065. Now, we can substitute these values into the formula.
I=Prt
828.75=P( 0.065)( 1.5)
828.75=P(0.0975)
828.75/0.0975=P(0.0975)/0.0975
â–Ľ
Calculate quotient
82 875100/97510 000=P(0.0975)/0.0975
33154/39400=P(0.0975)/0.0975
3315/4* 400/39=P(0.0975)/0.0975
3315* 400/4* 39=P(0.0975)/0.0975
1 326 000/156=P(0.0975)/0.0975
8500=P(0.0975)/0.0975
â–Ľ
Simplify right-hand side
8500=P(0.0975/0.0975)
8500=P(1)
8500=P
P=8500
The principal is $ 8500. We can add this information to the table.
Principal Annual Interest Rate Time Simple Interest
$12 000 4.25 % 5 years $2550
$ 8500 6.5 % 18 months $828.75