Answer:
Interest rate ( <em>r </em>) = 15.38% or 0.1538
Step-by-step explanation:
Given the principal (P) = $6,000, and the simple interest of $769 earned after 10 months:
We can determine the interest rate (<em>r</em> ) by creating its formula algebraically, then use the equation to solve for its value.
Using the simple interest formula,
<em>I </em>=<em> P </em>× <em>r </em>×<em> t </em>
where:
I = interest amount = $769
P = present value of the principal = $6,000
r = interest rate
t = time = 10/12 (10 months out of 12 months) = 0.83333
I = P × r × t
Divide both sides by P × t:
I / ( P × t ) = P × t × r / ( P × t )
I / ( P × t ) = r
Therefore, the formula for the interest rate is:<em> </em><em>r</em> = <em>I</em> / ( <em>P</em> × <em>t</em> )
Substitute the given values into the formula to solve for r:
r = I / ( P × t )
r = $769 / ($6,000 × 0.83333)
r = $769/ 4,999.99999
r = 0.1538 or 15.38%
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