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Zoe takes out a discounted loan for $1,200 at a simple interest rate of 6%, but only receives $1,020 into her bank account. What's the duration of the loan? Give your answer in months to the nearest month. Do not include the units in your answer.

Respuesta :

Assuming the interest rate is yearly, we can determine the duration of of the loan by solving the following equation for t, which comes from the formula for simple interest:

[tex]1200-1020=(\frac{t}{12})\cdot0.06\cdot1200[/tex][tex]180=(\frac{t}{12})\cdot72[/tex][tex]\frac{180}{72}=\frac{t}{12}[/tex][tex]2.5=\frac{t}{12}[/tex][tex]2.5\cdot12=t[/tex][tex]30=t[/tex]

So the duration of the loan is 30 months.

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