Larry came up a little short one month at bill paying time and had to take out a title loan on his car at Check Casher's, Inc. He borrowed $260, and 3 weeks later he paid off the note for $297.50. What was the annual simple interest rate on this title loan?

Question
Ratios, rates, proportions
asked 2021-03-05
Larry came up a little short one month at bill paying time and had to take out a title loan on his car at Check Casher's, Inc. He borrowed $260, and 3 weeks later he paid off the note for $297.50. What was the annual simple interest rate on this title loan?

Answers (1)

2021-03-06
The interest is: \(\displaystyle{I}=\${297.50}-\${260}=\${37.50}\)
Substitute P=$260 and \(\displaystyle{t}=\frac{{3}}{{52}}\) (3 weeks out of 52 weeks in a year) the solve for r: \(\displaystyle\${37.50}=\${260}{\left({r}\right)}\cdot\frac{{3}}{{52}}\)
Divide both sides by $260: \(\displaystyle\frac{{37.50}}{{260}}={\left(\frac{{3}}{{52}}\right)}{r}\)
Multiply both sides by \(\displaystyle\frac{{52}}{{3}}:\) \(\displaystyle{\left(\frac{{37.50}}{{260}}\right)}\cdot{\left(\frac{{52}}{{3}}\right)}={r}\) 2.5=r
In percentage, r=250%
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