Certainly! To solve for the rate [tex]\( r \)[/tex] in a simple interest problem, we use the formula for simple interest:
[tex]\[ I = P \times r \times t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest amount.
- [tex]\( P \)[/tex] is the principal amount.
- [tex]\( r \)[/tex] is the rate of interest per period.
- [tex]\( t \)[/tex] is the time the money is invested or borrowed for.
Given:
- [tex]\( I = \$290.50 \)[/tex]
- [tex]\( P = \$1000 \)[/tex]
- [tex]\( t = 7 \)[/tex] years
We are asked to find the rate [tex]\( r \)[/tex], to do this we rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{I}{P \times t} \][/tex]
Plugging in the values:
[tex]\[ r = \frac{290.50}{1000 \times 7} \][/tex]
First, calculate the denominator:
[tex]\[ 1000 \times 7 = 7000 \][/tex]
Now divide the interest by this value:
[tex]\[ r = \frac{290.50}{7000} = 0.0415 \][/tex]
The rate [tex]\( r \)[/tex] is 0.0415 when expressed as a decimal. To convert this to a percentage, we multiply by 100:
[tex]\[ r_{\text{percentage}} = 0.0415 \times 100 = 4.15\% \][/tex]
Thus, the rate of interest is [tex]\( 4.15\% \)[/tex].
We compare this to the given options:
- [tex]\( 1.45 \% \)[/tex]
- [tex]\( 4.15 \% \)[/tex]
- [tex]\( 28.85 \% \)[/tex]
- [tex]\( 41.5 \% \)[/tex]
The closest match and correct answer is:
[tex]\[ r = 4.15\% \][/tex]
