Susan invests 3 times as much money at 7% as she does at 4%. If her total interest after 1 year is $1250, how much does she have invested at each rate?
amount invested at 4% --- x
amount invested at 7% ---- 3x
solve for x then back-substitute :
.04x + .07(3x) = 1250
To find out how much Susan has invested at each rate, let's assume she invested 'x' dollars at 4%.
According to the problem, she has invested 3 times as much money at 7% as she has at 4%. So, she has invested 3x dollars at 7%.
Interest is calculated by multiplying the principal amount by the interest rate. We can use this formula to set up an equation to solve for the unknown variables.
At 4% interest, the interest earned would be (0.04 * x) dollars.
At 7% interest, the interest earned would be (0.07 * 3x) dollars.
According to the problem, the total interest earned after 1 year is $1250. So, we can set up the equation:
(0.04 * x) + (0.07 * 3x) = 1250
Simplifying the equation gives:
0.04x + 0.21x = 1250
0.25x = 1250
x = 1250 / 0.25
x = 5000
Therefore, Susan has $5000 invested at 4% and 3 * $5000 = $15000 invested at 7%.
Let's assume Susan has invested x dollars at 4% interest rate.
Then, she has invested 3x dollars at 7% interest rate.
The total interest earned from the 4% investment is 4% of x dollars,
which is 0.04 * x = 0.04x dollars.
The total interest earned from the 7% investment is 7% of 3x dollars,
which is 0.07 * (3x) = 0.21x dollars.
According to the problem, the total interest earned is $1250.
So, the equation becomes: 0.04x + 0.21x = 1250.
Combining like terms, we get: 0.25x = 1250.
Dividing both sides of the equation by 0.25, we find: x = 1250 / 0.25.
Calculating this, we find that x = $5000.
Therefore, Susan has invested $5000 at 4% and $15,000 (3 times $5000) at 7%.