The graph below shows the amount of money in one of Marie's savings accounts over several years. If Marie's savings continue to grow at the same rate as shown in the graph, how much money will she have saved by year 5 in this account?
The x axis of the graph is the years 0-4 and the y axis is the amount in savings from $2000-$2700. The points (0, $2000), (1, $2100), (2, $2250), (3, $2315), and (4, $2431) are marked on the graph. I know the formula and what to do to get how much money she will have, but I just need help finding the percentage, I can't seem to figure it out.
since the growth is increasing, there should be a common ratio between years
2100/2000 = 1.05
2250/2100 = 1.07
2315/2250 = 1.03
2431/2315 = 1.05
Seems kind of erratic, but maybe the best fit is 1.05 = 5% growth
To find the percentage increase between two consecutive years, you can use the formula:
Percentage increase = ((New amount - Old amount) / Old amount) * 100
Let's take the data for years 0 and 1:
New amount = $2100
Old amount = $2000
Percentage increase = ((2100 - 2000) / 2000) * 100
= (100 / 2000) * 100
= 0.05 * 100
= 5%
So, the percentage increase between years 0 and 1 is 5%.
Similarly, you can calculate the percentage increase between the other pairs of consecutive years.
To find the percentage increase between two values, you can use the following formula:
Percentage increase = ((new value - old value) / old value) * 100
In this case, to find the percentage increase between each year, you can calculate it using the values provided on the y-axis.
For example, between year 0 and year 1, Marie's savings increased from $2000 to $2100. Plugging these values into the formula, we get:
Percentage increase = (($2100 - $2000) / $2000) * 100
Percentage increase = ($100 / $2000) * 100
Percentage increase = 0.05 * 100
Percentage increase = 5%
Similarly, you can calculate the percentage increase for each year and use that to estimate the savings in year 5.
Between year 0 and year 1: 5% increase
Between year 1 and year 2: 7.14% increase (calculated in the same way)
Between year 2 and year 3: 2.89% increase
Between year 3 and year 4: 4.97% increase
To estimate the savings in year 5, we can assume that the same rate of increase continues. So, from year 4 to year 5, we can apply a 4.97% increase to the savings in year 4.
Savings in year 4: $2431
Percentage increase: 4.97%
Estimated savings in year 5 = $2431 + (4.97% of $2431)
To find 4.97% of $2431, you can use the formula:
4.97 / 100 = x / 2431
Cross-multiplying: 4.97 * 2431 = 100 * x
12081.07 = 100 * x
Now, divide both sides by 100:
x = 12081.07 / 100
x = 120.81
Estimated savings in year 5 = $2431 + $120.81
Estimated savings in year 5 = $2551.81
Therefore, based on the given data and assuming the same rate of increase, Marie will have approximately $2551.81 saved by year 5 in this account.