The interest rate at which Jack invested the $500 is 3%
The process for arriving at the above interest is as follows:
The given parameters:
The amount invested by Jack, at interest rare, r, P₁ = $500
The amount he invested at one-half percent higher, (r + 0.5), P₂ = $2,000
The total interest he receives in 1 year, S.I. = $85
The required parameters:
The interest rate at which he invested the $500, r
Method;
Solve for the interest rate using the interest rate formula
The formula for finding the simple interest, S. I. is given as follows:
[tex]S.I. = \mathbf{\dfrac{P \times R \times T}{100}}[/tex]
From the details of the question, we get;
[tex]S.I. = \mathbf{\dfrac{P_1 \times r \times t}{100}+ \dfrac{P_2 \times (r+0.5) \times t}{100}}[/tex]
Plugging in the values gives;
[tex]\mathbf{85} = \dfrac{500 \times r \times 1}{100}+ \dfrac{2000 \times (r+0.5) \times 1}{100} = \mathbf{ 25\cdot r + 10}[/tex]
∴ 25·r = 85 - 10 = 75
r = 75/25 = 3
The interest rate, S.I., at which the $500 is invested, r = 3%
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