Math / Algebra

QuestionAmelia invests money in an account paying simple interest. She invests $\$ 100$ and no money is added or removed from the investment. After one year, she has $\$ 101$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

Studdy Solution

STEP 1

1. Amelia invests $100 in an account with simple interest.<br />2. No additional money is added or removed from the account.<br />3. After one year, the total amount in the account is$ 101.
4. We need to find the simple interest rate as a percentage per year.

STEP 2

1. Understand the formula for simple interest.
2. Identify the known values and the unknown variable.
3. Substitute the known values into the simple interest formula.
4. Solve for the unknown variable, which is the interest rate.
5. Convert the interest rate to a percentage.

STEP 3

Understand the formula for simple interest.
The formula for simple interest is given by:
$A = P(1 + rt)$
where: - $A$ is the total amount after time $t$ , - $P$ is the principal amount (initial investment), - $r$ is the interest rate per time period, - $t$ is the time period.

STEP 4

Identify the known values and the unknown variable.
From the problem: - $A = 101$ - $P = 100$ - $t = 1$ year - $r$ is the unknown variable (interest rate).

STEP 5

Substitute the known values into the simple interest formula.
$101 = 100(1 + r \cdot 1)$

STEP 6

Solve for the unknown variable, which is the interest rate $r$ .
First, simplify the equation:
$101 = 100(1 + r)$
Divide both sides by 100 to isolate the term with $r$ :
$\frac{101}{100} = 1 + r$
Subtract 1 from both sides:
$\frac{101}{100} - 1 = r$
$r = \frac{101}{100} - \frac{100}{100}$
$r = \frac{1}{100}$

STEP 7

Convert the interest rate to a percentage.
Since $r = \frac{1}{100}$ , to convert it to a percentage, multiply by 100:
$r = \frac{1}{100} \times 100 = 1\%$
The simple percent interest per year is:
$\boxed{1} \%$

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QuestionAmelia invests money in an account paying simple interest. She invests $\$ 100$ and no money is added or removed from the investment. After one year, she has $\$ 101$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

Studdy Solution

STEP 1

1. Amelia invests $100 in an account with simple interest.<br />2. No additional money is added or removed from the account.<br />3. After one year, the total amount in the account is$ 101.
4. We need to find the simple interest rate as a percentage per year.

STEP 2

1. Understand the formula for simple interest.
2. Identify the known values and the unknown variable.
3. Substitute the known values into the simple interest formula.
4. Solve for the unknown variable, which is the interest rate.
5. Convert the interest rate to a percentage.

STEP 3

Understand the formula for simple interest.
The formula for simple interest is given by:
$A = P(1 + rt)$
where: - $A$ is the total amount after time $t$ , - $P$ is the principal amount (initial investment), - $r$ is the interest rate per time period, - $t$ is the time period.

STEP 4

Identify the known values and the unknown variable.
From the problem: - $A = 101$ - $P = 100$ - $t = 1$ year - $r$ is the unknown variable (interest rate).

STEP 5

Substitute the known values into the simple interest formula.
$101 = 100(1 + r \cdot 1)$

STEP 6

STEP 7

Convert the interest rate to a percentage.
Since $r = \frac{1}{100}$ , to convert it to a percentage, multiply by 100:
$r = \frac{1}{100} \times 100 = 1\%$
The simple percent interest per year is:
$\boxed{1} \%$

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QuestionAmelia invests money in an account paying simple interest. She invests $100\$ 100$100 and no money is added or removed from the investment. After one year, she has $101\$ 101$101. What is the simple percent interest per year?Answer □\square□ \% Submit Answer

Studdy Solution

STEP 1

STEP 2

1. Understand the formula for simple interest.2. Identify the known values and the unknown variable.3. Substitute the known values into the simple interest formula.4. Solve for the unknown variable, which is the interest rate.5. Convert the interest rate to a percentage.

STEP 3

STEP 4

Identify the known values and the unknown variable.From the problem: - A=101 A = 101 A=101 - P=100 P = 100 P=100 - t=1 t = 1 t=1 year - r r r is the unknown variable (interest rate).

STEP 5

Substitute the known values into the simple interest formula.101=100(1+r⋅1) 101 = 100(1 + r \cdot 1) 101=100(1+r⋅1)

STEP 6

STEP 7

Convert the interest rate to a percentage.Since r=1100 r = \frac{1}{100} r=1001​, to convert it to a percentage, multiply by 100:r=1100×100=1% r = \frac{1}{100} \times 100 = 1\% r=1001​×100=1%The simple percent interest per year is:1% \boxed{1} \% 1​%

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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.

QuestionAmelia invests money in an account paying simple interest. She invests $\$ 100$ and no money is added or removed from the investment. After one year, she has $\$ 101$ . What is the simple percent interest per year?
Answer $\square$ \% Submit Answer

1. Understand the formula for simple interest.
2. Identify the known values and the unknown variable.
3. Substitute the known values into the simple interest formula.
4. Solve for the unknown variable, which is the interest rate.
5. Convert the interest rate to a percentage.

Identify the known values and the unknown variable.
From the problem: - $A = 101$ - $P = 100$ - $t = 1$ year - $r$ is the unknown variable (interest rate).

Substitute the known values into the simple interest formula.
$101 = 100(1 + r \cdot 1)$

Convert the interest rate to a percentage.
Since $r = \frac{1}{100}$ , to convert it to a percentage, multiply by 100:
$r = \frac{1}{100} \times 100 = 1\%$
The simple percent interest per year is:
$\boxed{1} \%$