Answer :
Final answer:
To find the original principal and the simple interest rate, set up a system of equations and solve for P and r. The original principal is $7,864 and the simple interest rate offered was approximately 13%.
Explanation:
To find the original principal and the simple interest rate, we can set up a system of equations based on the given information. Let's call the original principal P and the simple interest rate r. According to the given information, we have:
P + Pr(2 + 3/12) = 12,947
P + Pr(2 + 3/12 + 2 + 3/12) = 14,913
Simplifying these equations, we have:
P + Pr(2.25) = 12,947
P + Pr(2.5) = 14,913
Subtracting the first equation from the second equation, we get:
Pr(2.5) - Pr(2.25) = 14,913 - 12,947
Simplifying further, we have:
Pr(0.25) = 1,966
Dividing both sides by 0.25, we get:
Pr = 1,966 / 0.25
Pr = 7,864
So, the original principal is $7,864. To find the simple interest rate, we can substitute the value of the original principal into one of the equations:
7,864 + 7,864r(2.25) = 12,947
Simplifying this equation gives:
7,864r(2.25) = 5,083
Dividing both sides by 7,864(2.25), we get:
r = 5,083 / (7,864 × 2.25)
r ≈ 0.13 (or 13%)
Therefore, the original principal was $7,864 and the simple interest rate offered was approximately 13%.
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