Answer:
He invested $8500 with rate 3 1/5%
He invested $3000 with rate 3%
Step-by-step explanation:
* Lets revise the rule of the simple interest
- Simple interest I = PRT, where P in the money invested, R is the
interest rate and T is the time of investment
- Phyllis invested $11,500
- A portion earning a simple interest rate of 3 1/5% (3.2%) per year
- The rest earning a rate of 3% per year
- After one year the total interest earned on these investments
was $362.00
- We need to find the amount of money invested in each rate
* Assume that he invested $x with rate 3 1/5% and $y with rate 3%
∵ He invested $11,500 in both rates
∴ x + y = 11,500 ⇒ (1)
∵ He invested $x with 3 1/5%
∵ P = $x
∵ R = 3.2/100 = 0.032
∵ T = 1
∴ [tex]I_{1}=x(0.032)(1)[/tex]
∴ [tex]I_{1}=0.032x[/tex]
∵ He invested $y with 3%
∵ P = $y
∵ R = 3/100 = 0.03
∵ T = 1
∴ [tex]I_{2}=y(0.03)(1)[/tex]
∴ [tex]I_{2}=0.03y[/tex]
∵ The total interest was $362.00
- The total interest = [tex]I_{1}[/tex] + [tex]I_{2}[/tex]
∴ 0.032x + 0.03y = 362.00 ⇒ (2)
We have system of equations
x + y = 11,500 ⇒ (1)
0.032x + 0.03y = 362.00 ⇒ (2)
Multiply equation (1) by -0.03 to eliminate y
-0.03x - 0.03y = 345 ⇒ (3)
Add equations (2) and (3)
0.002x = 17
Divide both sides by 0.002
x = 8500
Substitute the value of x in equation (1)
8500 + y = 11,500
Subtract 8500 from both sides
y = 3000
* He invested $8500 with rate 3 1/5%
* He invested $3000 with rate 3%
