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Question 1199783: Phyllis invested $13,500, a portion earning a simple interest rate of 5 1/5% per year and the rest earning a rate of 5% per year. After 1 year the total interest earned on these investments was $692. How much money did she invest at each rate?
Answer by ikleyn(52767)   (Show Source):
You can put this solution on YOUR website! .
Phyllis invested $13,500, a portion earning a simple interest rate of 5 1/5% per year
and the rest earning a rate of 5% per year.
After 1 year the total interest earned on these investments was $692.
How much money did she invest at each rate?
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Let x be the amount invested at 5 1/5% (in what follows, I will write 5.2%, for simplicity).
Then the amount invested at 5% is the rest (13500-x) dollars.
As you read the problem, write the total annual interest equation
0.052x + 0.05*(13500-x) = 692 dollars.
Simplify, express x and get the answer
0.052x + 0.05*13500 - 0.05x = 692
0.052x - 0.05x = 692 - 0.05*13500
0.002x = 17
x = 17/0.002 = 17000/2 = 8500.
ANSWER. $8500 invested at 5.2%; the rest $13500 - $8500 = $5000 invested at 5%.
CHECK. 0.052*8500 + 0.05*5000 = 692 dollars, the total annual interest. ! Correct !
Solved.
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