To find the amount of interest earned each year with simple interest, we can use the information given by the points (3, 21) and (8, 56) on the graph.
In these points:
- The first number represents the number of years since the deposit.
- The second number represents the total account balance after those years.
-
Calculate the total interest earned for each point:
-
For the point (3, 21):
- The account balance after 3 years is $21.
- The initial deposit was $350, so the interest earned over 3 years is: \[ \text{Interest} = \text{Account Balance} - \text{Initial Deposit} = 21 - 350 = -329 \text{ (this seems incorrect; let’s analyze again)} \]
-
For the point (8, 56):
- The account balance after 8 years is $56.
- The interest earned over 8 years is: \[ \text{Interest} = 56 - 350 = -294 \]
-
-
Calculate the change in interest between the two points:
- The change in account balance from year 3 to year 8 is: \[ 56 - 21 = 35 \]
- The change in time is: \[ 8 - 3 = 5 \text{ years} \]
-
Calculate the amount of interest earned per year:
- The interest earned per year can be found by dividing the total change in balance by the change in time: \[ \text{Interest per year} = \frac{35}{5} = 7 \]
So, the amount of interest you earn each year is $7.
- Final Result:
- The total simple interest earned can further be confirmed by multiplying the interest earned per year by the number of years: \[ \text{Total Interest} = 7 \text{ (interest per year)} \times t \text{ (years)} \]
Thus, the solution is that the amount of interest earned each year is \(\mathbf{7}\) dollars.
9 answers