Math / Algebra

QuestionTHINKING - don't forget your concluding statements Peter invested in a GIC that paid $3.25 \%$ simple interest. In 36 months, he earned $\$ 485$ interest. $\begin{array}{l} =485 \\ =? \end{array}$ $\begin{array}{l} =3.25 \\ =36 \end{array}$

Studdy Solution

STEP 1

1. Peter invested in a Guaranteed Investment Certificate (GIC) that pays simple interest.
2. The interest rate is $3.25\%$ .
3. The time period for the investment is 36 months.
4. The interest earned is $\$485$ .
5. We need to find the principal amount invested.

STEP 2

1. Understand the formula for simple interest.
2. Convert the time period from months to years.
3. Set up the equation using the simple interest formula.
4. Solve for the principal amount.

STEP 3

Understand the formula for simple interest. The formula for simple interest is given by:
$I = P \times r \times t$
where: - $I$ is the interest earned, - $P$ is the principal amount (the initial amount of money), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years.

STEP 4

Convert the time period from months to years. Since there are 12 months in a year, we convert 36 months to years:
$t = \frac{36}{12} = 3 \text{ years}$

STEP 5

Set up the equation using the simple interest formula. Substitute the known values into the formula:
$485 = P \times \left(\frac{3.25}{100}\right) \times 3$

STEP 6

Solve for the principal amount $P$ .
First, simplify the equation:
$485 = P \times 0.0325 \times 3$
$485 = P \times 0.0975$
Now, divide both sides by 0.0975 to solve for $P$ :
$P = \frac{485}{0.0975}$
$P \approx 4974.36$
Therefore, the principal amount invested by Peter is approximately:
$\boxed{4974.36}$

Was this helpful?

QuestionTHINKING - don't forget your concluding statements Peter invested in a GIC that paid $3.25 \%$ simple interest. In 36 months, he earned $\$ 485$ interest. $\begin{array}{l} =485 \\ =? \end{array}$ $\begin{array}{l} =3.25 \\ =36 \end{array}$

Studdy Solution

STEP 1

1. Peter invested in a Guaranteed Investment Certificate (GIC) that pays simple interest.
2. The interest rate is $3.25\%$ .
3. The time period for the investment is 36 months.
4. The interest earned is $\$485$ .
5. We need to find the principal amount invested.

STEP 2

1. Understand the formula for simple interest.
2. Convert the time period from months to years.
3. Set up the equation using the simple interest formula.
4. Solve for the principal amount.

STEP 3

Understand the formula for simple interest. The formula for simple interest is given by:
$I = P \times r \times t$
where: - $I$ is the interest earned, - $P$ is the principal amount (the initial amount of money), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years.

STEP 4

Convert the time period from months to years. Since there are 12 months in a year, we convert 36 months to years:
$t = \frac{36}{12} = 3 \text{ years}$

STEP 5

Set up the equation using the simple interest formula. Substitute the known values into the formula:
$485 = P \times \left(\frac{3.25}{100}\right) \times 3$

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionTHINKING - don't forget your concluding statements Peter invested in a GIC that paid 3.25%3.25 \%3.25% simple interest. In 36 months, he earned $485\$ 485$485 interest. =485=?\begin{array}{l} =485 \\ =? \end{array}=485=?​ =3.25=36\begin{array}{l} =3.25 \\ =36 \end{array}=3.25=36​

Studdy Solution

STEP 1

1. Peter invested in a Guaranteed Investment Certificate (GIC) that pays simple interest.2. The interest rate is 3.25%3.25\%3.25%.3. The time period for the investment is 36 months.4. The interest earned is $485\$485$485.5. We need to find the principal amount invested.

STEP 2

1. Understand the formula for simple interest.2. Convert the time period from months to years.3. Set up the equation using the simple interest formula.4. Solve for the principal amount.

STEP 3

STEP 4

Convert the time period from months to years. Since there are 12 months in a year, we convert 36 months to years:t=3612=3 years t = \frac{36}{12} = 3 \text{ years} t=1236​=3 years

STEP 5

Set up the equation using the simple interest formula. Substitute the known values into the formula:485=P×(3.25100)×3 485 = P \times \left(\frac{3.25}{100}\right) \times 3 485=P×(1003.25​)×3

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionTHINKING - don't forget your concluding statements Peter invested in a GIC that paid $3.25 \%$ simple interest. In 36 months, he earned $\$ 485$ interest. $\begin{array}{l} =485 \\ =? \end{array}$ $\begin{array}{l} =3.25 \\ =36 \end{array}$

1. Peter invested in a Guaranteed Investment Certificate (GIC) that pays simple interest.
2. The interest rate is $3.25\%$ .
3. The time period for the investment is 36 months.
4. The interest earned is $\$485$ .
5. We need to find the principal amount invested.

1. Understand the formula for simple interest.
2. Convert the time period from months to years.
3. Set up the equation using the simple interest formula.
4. Solve for the principal amount.

Convert the time period from months to years. Since there are 12 months in a year, we convert 36 months to years:
$t = \frac{36}{12} = 3 \text{ years}$

Set up the equation using the simple interest formula. Substitute the known values into the formula:
$485 = P \times \left(\frac{3.25}{100}\right) \times 3$