To find the time it takes for a principal to earn a certain amount of simple interest at a given rate, we use the simple interest formula:
\[ I = P \cdot R \cdot T \]
Where:
- \( I \) is the interest earned,
- \( P \) is the principal amount,
- \( R \) is the rate of interest per year (in decimal form),
- \( T \) is the time in years.
Here, we are given:
\[ I = \$1260 \]
\[ P = \$7200 \]
\[ R = 7\% = 0.07 \text{ (7% converted to a decimal)} \]
We need to solve for \( T \), so we rearrange the formula to solve for \( T \):
\[ T = \frac{I}{P \cdot R} \]
Now plug in the values:
\[ T = \frac{1260}{7200 \cdot 0.07} \]
Calculate the denominator first:
\[ 7200 \cdot 0.07 = 504 \]
Now plug that into the equation for \( T \):
\[ T = \frac{1260}{504} \]
Now perform the division:
\[ T = 2.5 \text{ years} \]
The options provided are:
a) 4 years
b) 5 years
c) 2 years
d) 2.5 years
The correct answer matches none of the single-year options because \( T = 2.5 \) years. However, option d) seems to be half-typed "2y," which could potentially be mistaken for an attempt to write "2.5 years."
Given this context, the most accurate answer based on the calculation would be option d), assuming it was intended to represent "2.5 years." If options only allowed for full years, there would be no exact match, but since 2.5 is closest to option d), we would select that as our answer.
