# To purchase new furniture, the owner of a restaurant borrowed $5,000.00 for 2 ye and paid$350.00 simple interest on the loan. What rate of interest did she pay?

Dec 19, 2016

See the explanation: There is ambiguity in the question.

#### Explanation:

$\textcolor{red}{\text{Possible ambiguity in the question}}$

Was the interest the total paid of the 2 years or was it the amount paid each year for a period of 2 years. If the latter then she paid $700.00 as a total. $\textcolor{b l u e}{\text{Condition 2 is the most likely intended meaning}}$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Initial condition }}$Expressing the total interest over the full time span as a fraction of the principle sum gives us: $\frac{350}{5000}$$\textcolor{b l u e}{\text{Determine the percentage interest in total over the full time span}}$To change this to a percentage of the principle sum we need to modify it such that the 5000 becomes 100. To change the 5000 into 100 divide it by 50. However, to maintain proportionality for multiply or divide what we do to the bottom we do to the top so we have: $\frac{350}{5000} \equiv \frac{350 \div 50}{5000 \div 50} = \frac{7}{100}$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Condition 1:- For the condition: $350 total paid over the 2 years}}$

color(brown)("Percentage paid annually was "1/2xx7/100 = 3.5/100 = 3.5%
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Condition 2:-For the condition:$350 total paid over 1 year}}\$

color(brown)("Percentage paid annually was "7/100 = 7%