You have a total of $10,000 to invest in two simple interest accounts. On one account the annual simple interest rate is 3.5%. On the second account the annual simple interest rate is 7.5%. If you earn $520 per year from these two investments, how much do you have invested in each account?
Make this chart:
| Amount invested | Rate | Amount of interest |
at lower rate | | | |
at higher rate | | | |
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Total | ||||||||| |
Let's let $x be the amount invested at the lower rate.
Then $10000-$x will be the amount invested at the higher rate,
and the total amount invested will be $10000. We fill those in:
| Amount invested | Rate | Amount of interest |
at lower rate | x | | |
at higher rate | 10000-x | | |
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Total | 10000 ||||||||| |
Fill in the rates as decimals:
Fill in the amount of interest by multiplying the rate by the amount invested
Fill in the total amount of interest received as $520
| Amount invested | Rate | Amount of interest |
at lower rate | x | .035 | .035x |
at higher rate | 10000-x | .075 | .075(10000-x) |
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Total | 10000 ||||||||| 520 |
The equation comes from:
+ =
.035x + .075(1000-x) = 520
Solve that and get x = $5750
Therefore the answer is:
x = $5750 at the lower rate of 3.5%
10000 - x = 10000 - 4250 = $4250 at 7.5%
Edwin