To determine the rate of interest [tex]\( r \)[/tex], we can use the formula for simple interest:
[tex]\[ I = P \times r \times t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( t \)[/tex] is the time period,
- [tex]\( r \)[/tex] is the rate of interest.
Given:
- [tex]\( I = 340 \)[/tex] dollars,
- [tex]\( P = 1,000 \)[/tex] dollars,
- [tex]\( t = 8 \)[/tex] years.
We need to solve for [tex]\( r \)[/tex]. Rearrange the simple interest formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{I}{P \times t} \][/tex]
Substitute the given values into the formula:
[tex]\[ r = \frac{340}{1,000 \times 8} \][/tex]
Calculate the value inside the fraction:
[tex]\[ 1,000 \times 8 = 8,000 \][/tex]
Thus,
[tex]\[ r = \frac{340}{8,000} \][/tex]
Simplify the fraction:
[tex]\[ r = 0.0425 \][/tex]
To express the rate as a percentage, multiply by 100:
[tex]\[ r \times 100 = 0.0425 \times 100 = 4.25\% \][/tex]
Therefore, the correct rate of interest [tex]\( r \)[/tex] is:
[tex]\[ \mathbf{4.25\%} \][/tex]
