Juanita's error lies in the formula she used to calculate the simple interest. The correct formula for calculating simple interest is:
\[ I = P \times r \times t \]
where:
- \( I \) is the interest earned,
- \( P \) is the principal amount (the initial amount of money borrowed or invested),
- \( r \) is the rate of interest (expressed as a decimal), and
- \( t \) is the time the money is borrowed or invested (in years).
In Juanita's equation:
\[ I = 600(7)(2) \]
she mistakenly used 7 as the interest rate in decimal form. The interest rate of 7% should be expressed as a decimal by dividing by 100, which gives:
\[ r = 0.07 \]
The correct calculation for the interest should have been:
\[ I = 600 \times 0.07 \times 2 \]
Calculating this:
\[ I = 600 \times 0.07 \times 2 = 600 \times 0.14 = 84 \]
So, the correct interest Juanita should have calculated is $84.
By using 7 instead of 0.07, Juanita's calculation would yield:
\[ I = 600 \times 7 \times 2 = 600 \times 14 = 8400 \]
This would be a gross overestimation of the interest. The error affects her calculation by giving her an incorrect result that is significantly higher than the actual interest she owes. Thus, she would believe she needs to pay $8400 in interest instead of the correct amount of $84, which could lead to significant financial misunderstanding or even distress.
1 answer