The combined yearly interest for x dollars invested at 12% and 30,000 - x dollars invested at 9% is
.12x + .09(30000-x)
To find the combined yearly interest for the two investments, we need to calculate the interest for each investment separately and then sum them together.
1. Calculate the interest for the first investment:
- The amount invested is x dollars.
- The interest rate is 12%.
- The formula to calculate interest is: Interest = Principal × Rate
- So, the interest for the first investment is: 0.12x
2. Calculate the interest for the second investment:
- The amount invested is 30,000 - x dollars.
- The interest rate is 9%.
- Using the same formula as before, the interest for the second investment is: 0.09(30,000 - x)
3. Add the interest from the two investments to get the combined yearly interest:
- Combined Yearly Interest = Interest for the first investment + Interest for the second investment
- Combined Yearly Interest = 0.12x + 0.09(30,000 - x)
So, the combined yearly interest for x dollars invested at 12% and 30,000 - x dollars invested at 9% is 0.12x + 0.09(30,000 - x).
To find the combined yearly interest for the given investments, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal amount (amount invested)
r = Interest rate
t = Time period (in years)
For the first investment at 12%, the principal amount is x dollars and the interest rate is 12%. Therefore, the interest can be calculated as:
I1 = x * 0.12
For the second investment at 9%, the principal amount is (30,000 - x) dollars and the interest rate is 9%. Therefore, the interest can be calculated as:
I2 = (30,000 - x) * 0.09
The combined interest would be the sum of I1 and I2:
Combined Interest = I1 + I2
= x * 0.12 + (30,000 - x) * 0.09
So, the combined yearly interest for the investments would be expressed as x * 0.12 + (30,000 - x) * 0.09.