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Two years ago, a sum of money was invested. Now, it is worth 12,947. If it is extended 2 years and 3 months, it will be 14,913. Find the original principal and the simple interest rate that was offered.

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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