Question 72419: during the early 1990's kelly invested 8000 into two different types of accounts within a bank certificates of deposit and savings account. For her accounts she received 8% interest for her certificates of deposit and 6% for her savings account. In total she earned 580 for the yeat. How much money was invested in each type of account?
Answer by bam878s(77)   (Show Source):
You can put this solution on YOUR website! Let x be the portion invested into the CD account (certificate of deposit)
Let y be the portion invested into the savings account.
Now we already know that x + y = 8000, so let's solve this equation for y.
x + y = 8000 => y = 8000 - x.
Now we know x is invested at 8% and y is invested at 6%. To find the amount each makes at the end of the year we take x(.08) + x. Note x(.08) is the amount of interest that is made on that amount at the end of the year. So we add x to this amount to get the total of x at the end of the year. Similarly for y, we have y(.06) + y.
Now let's re-write these equations.
x(.08) + x = x(1.08), and
y(.06) + y = y(1.06).
Now, since we know that 580 dollars was made on the TOTAL amount at the end of the year we know we end up with 8580.
Now we can write this:
x(1.08) + y(1.06) = 8580
Now, since we solved for y at the beginning, we can plug this value into this equation and solve for x.
x(1.08) + y(1.06) = 8580
x(1.08) + (8000-x)(1.06) = 8580 (multiply 8000-x by 1.06)
x(1.08) + 8480 - x(1.06) = 8580 (subtract 8480 from both sides)
x(1.08) - x(1.06) = 100 (subtract x terms on the left hand side)
x(.02) = 100 (divide both sides by .02)
x = 5000.
Now we can plug this value into the original equation to solve for y.
5000 + y = 8000
y = 3000.
So, 5000 was invested into the CD and 3000 was invested into the savings account.
I hope this helps!!
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