7. Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest
a. How much does she have in her account at the end of 3 years?
b. At what annual simple interest rate did the account grow? Show your work.
c. How many more dollars would she have in her account if the interest rate were 1% greater? Show your work.
8.The graph below was drawn with output on the vertical axis and input on the horizontal axis. What does this graph indicate about the relationship between the input and the output?
a. To find out how much Yvonne has in her account at the end of 3 years, we need to calculate the total amount (principal + interest). The formula for simple interest is:
Interest = Principal * Rate * Time
We know that the interest earned is $960 and the time is 3 years. We also know that the principal is $4,000. Plugging these values into the formula, we can solve for the rate:
960 = 4000 * Rate * 3
Dividing both sides of the equation by 12,000 gives:
Rate = 960 / 12,000
Simplifying this fraction gives:
Rate = 0.08 or 8%
b. To find the annual simple interest rate, we can rearrange the formula for simple interest:
Rate = Interest / (Principal * Time)
Plugging in the given values:
Rate = 960 / (4,000 * 3)
Simplifying this fraction gives the answer:
Rate = 0.08 or 8%
c. To calculate how many more dollars Yvonne would have in her account if the interest rate were 1% greater, we can use the formula for simple interest again. First, let's find the interest earned at the increased rate:
New Interest = Principal * (Rate + 0.01) * Time
Plugging in the values:
New Interest = 4,000 * (0.08 + 0.01) * 3
Simplifying this expression gives the new interest earned.
To find the difference in dollars, we subtract the original interest from the new interest:
Difference = New Interest - Original Interest
Substituting in the calculated values, we get the final answer.
8. Without the specific graph, it is difficult to provide a precise interpretation of the input-output relationship. However, typically, a graph with the output on the vertical axis and the input on the horizontal axis indicates how one variable or quantity changes (or varies) in relation to the other. It shows the relationship between the input and the output values and any patterns, trends, or associations present in the data. The slope or steepness of the graph can also provide information about the rate of change between the input and output variables.
1. Show your work, and a tutor will check it for you.
2. There's no graph.