# 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
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?

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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