Amelia's parents and grand parents have both opened savings accounts to save for Amelia's education this year. Amelia's parents' savings account earned 5% interest and her grandparents account earned 8% interest. This year the two savings accounts have earned a total of $460 in interest. At the beginning of the year, the two accounts were worth a total of $6400. Determine the current values of both savings account.
Let x be the parents' account value and y be the grandparents account value t the beginning of the year.
x (0.05) + y (0.08) = 460
x + y = 6400
x + 1.6 y = 9200
0.6 y = 2800
y = $4666.67
x = $1733.33
To get the current values, add the interest gained in the previous year.
To determine the current values of both savings accounts, we can start by setting up a system of equations based on the given information. Let's represent the parents' account value at the beginning of the year as x, and the grandparents' account value as y.
From the given information, we know:
Equation 1: The parents' account earned 5% interest, so the interest earned from their account is 0.05x.
Equation 2: The grandparents' account earned 8% interest, so the interest earned from their account is 0.08y.
Equation 3: The total interest earned from both accounts is $460.
Equation 4: The total value of both accounts at the beginning of the year is $6400.
We can set up the equations as follows:
0.05x + 0.08y = 460 (Equation 1)
x + y = 6400 (Equation 2)
Now, we solve this system of equations to find the current values of both savings accounts.
Multiply Equation 1 by 100 to remove the decimals:
5x + 8y = 46000 (Equation 1 multiplied by 100)
x + y = 6400 (Equation 2)
Now, we can solve this system of equations using the elimination method:
Multiply Equation 2 by 5 to make the coefficient of x the same as Equation 1:
5x + 5y = 32000 (Equation 2 multiplied by 5)
5x + 8y = 46000 (Equation 1 multiplied by 100)
Subtract Equation 2 from Equation 1:
(5x + 8y) - (5x + 5y) = 46000 - 32000
3y = 14000
y = 14000/3
y ≈ $4666.67
Substitute the value of y back into Equation 2 to find x:
x + $4666.67 = 6400
x ≈ $1733.33
Therefore, the current value of the parents' savings account is approximately $1733.33, and the current value of the grandparents' savings account is approximately $4666.67.
To find the updated values, add the interest gained in the previous year to these amounts.