SOLUTION: A total of $9000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $520?
Algebra.Com
Question 1195905: A total of $9000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $520?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
x = amount invested at 5%
9000-x = remaining amount invested at 15%
Assuming simple interest is involved (instead of compound interest), we then use this formula
i = P*r*t
where,
P = principal aka deposit
r = interest rate in decimal form
t = number of years
The portion invested at 5% will get us this amount of interest
i = P*r*t
i = x*0.05*1
i = 0.05x
which is what we'll have at the end of the year from this one investment.
The other account yields...
i = P*r*t
i = (9000-x)*0.15*1
i = 1350-0.15x
These two interest subtotals add to the stated annual interest of $520
(0.05x) + (1350-0.15x) = 520
-0.10x + 1350 = 520
-0.10x = 520-1350
-0.10x = -830
x = -830/(-0.10)
x = 8300 dollars was invested at a 5% interest rate
9000-x = 9000 - 8300 = 700 dollars was invested at a rate of 15%
Answers:
Amount invested at 5% = $8300
Amount invested at 15% = $700
Check:
8300*0.05+700*0.15 = 415 + 105 = 520
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Here is an informal method for solving this kind of problem that is fast and easy if the numbers are "nice".
(1) All $9000 invested at 5% would earn $450 interest; all at 15% would earn $1350 interest.
(2) Perhaps using a number line, look where the actual interest of $520 lies between $450 and $1350: 450 to 520 is a difference of 70; 450 to 1350 is a difference of 900; 520 is 70/900 = 7/90 of the way from 450 to 1350.
(3) That means 7/90 of the total was invested at the higher rate.
ANSWER: 7/90 of $9000, or $700, was invested at 15%; the other $8300 at 5%.
CHECK: .05(8300)+.15(700) = 415+105 = 520
RELATED QUESTIONS
A total of
$9000
$9000
is invested: part at
6%
6%
and the remainder at
11%... (answered by greenestamps)
a total of $7000 is invested: part at 5% and the remainder at 9%. how much is invested at (answered by FrankM)
A total of $8000 is invested, part at 6% and the remainder at 9%. How much is invested at (answered by checkley75)
A total of $6000 is invested. Part at 8% and the remainder at 14%. How much is invested... (answered by htmentor)
A total of $7000 is invested: part at 7% and the remainder at 11%. How much is invested... (answered by checkley79)
a total of $7000 is invested: part at 9% and the remainder at 11%. How much is invested... (answered by mananth)
A total of $6000 is invested: part at 9% and the remainder at 14%. How much is invested... (answered by mananth)
A total of $5000 is invested: part at 7% and the remainder at 12%. How much is invested... (answered by srinivas.g)
A total of
$7000 is invested: part at
7% and the remainder at
12%
.
How much is... (answered by jorel1380)