$100,000 is divided into two investments with annual returns of 4% and 7.5%. find the amount invested at the lower rate if the total income at the end of the year is $5050?
work with the principal and the interest.
x * 0.04 + (100000-x) * 0.075 = 5050
.04x + 7500 - .075x = 5050
.035x = 2450
x = 70000
70000 * .04 + 30000 * .075 = 5050
To find the amount invested at the lower rate, let's assume that the amount invested at the lower rate is x.
The amount invested at the higher rate would then be $100,000 - x.
At a 4% annual return, the income from the amount invested at the lower rate is x * 0.04.
At a 7.5% annual return, the income from the amount invested at the higher rate is (100,000 - x) * 0.075.
The total income at the end of the year is given as $5050.
So, we can set up the following equation:
x * 0.04 + (100,000 - x) * 0.075 = 5050
Now, let's solve for x:
0.04x + 7500 - 0.075x = 5050
-0.035x = -2450
x = -2450 / -0.035
x ≈ 70000
Therefore, the amount invested at the lower rate is approximately $70,000.