Questions: After 8 years, Sheila's account earned 900 in interest. If the interest rate (in decimal form) is 0.08 , how much did Sheila initially invest?

After 8 years, Sheila's account earned 900 in interest. If the interest rate (in decimal form) is 0.08 , how much did Sheila initially invest?

Transcript text: After 8 years, Sheila's account earned $900 in interest. If the interest rate (in decimal form) is 0.08 , how much did Sheila initially invest?

Solution

Solution Steps

To find out how much Sheila initially invested, we need to use the formula for simple interest, which is \( I = P \times r \times t \), where \( I \) is the interest earned, \( P \) is the principal amount (initial investment), \( r \) is the interest rate, and \( t \) is the time in years. We need to solve this formula for \( P \).

Rearrange the formula to solve for \( P \): \( P = \frac{I}{r \times t} \).
Substitute the known values into the formula: \( I = 900 \), \( r = 0.08 \), and \( t = 8 \).

Step 1: Identify 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 (initial investment),
\( r \) is the interest rate,
\( t \) is the time in years.

Step 2: Rearrange the Formula to Solve for \( P \)

To find the initial investment \( P \), rearrange the formula: \[ P = \frac{I}{r \times t} \]

Step 3: Substitute the Known Values

Substitute the given values into the formula:

\( I = 900 \)
\( r = 0.08 \)
\( t = 8 \)

\[ P = \frac{900}{0.08 \times 8} \]

Step 4: Calculate the Initial Investment

Perform the calculation: \[ P = \frac{900}{0.64} = 1406.25 \]

Final Answer

The initial investment Sheila made is \(\boxed{1406.25}\).

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Answered

In a test of the effects of eating a vegetarian diet on cholesterol, one group of 55 randomly selected subjects undergoes a treatment consisting of a vegetarian diet while another group of 58 randomly selected subjects eats a non-vegetarian diet. The researchers doing the measurements of cholesterol are aware of which participants receive the treatment and which do not receive it. Identify any problems that are likely to cause confounding and explain how the problems could be avoided. Identify any problems that are likely to cause confounding. Select all that apply. A. There is likely to be an experimenter effect in this study because the researcher making the cholesterol measurements will influence the subjects by knowing which participants eat a vegetarian diet and which participants do not. B. The groups are so small that confounding is likely to be introduced by the select of the group subjects. C. If there are differences in the measurements of cholesterol, there is no way to know if the differences are attributable to the treatment (eating a vegetarian diet) or to the height of the participant. D. There is likely to be a placebo effect in this study because the subjects know whether they are eating a vegetarian or non-vegetarian diet. E. There is no control group. Explain how the problems could be avoided. Select all that apply. A. The size of the groups should be increased to eliminate the possibility of a biasє sample. B. Differences in the measurements of cholesterol can be correctly attributed to eating vegetarian by giving the vegetarian diet treatment to half of the short subjects and half of the tall subjects and by not giving the vegetarian diet treatment to the other subjects. C. Unfortunately, there is no way to eliminate the placebo effect in this study. D. The study's subjects should not be aware whether they receive the vegetarian diet treatment or not. E. The researchers doing the cholesterol measurements should not be aware of which participants eat a vegetarian diet or do not eat a vegetarian diet.

< Previous Next >

Thank you for your feedback.

Copied!