Question

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.

Answer 1

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:

`1200-1020=((t)/(12))\cdot0.06\cdot1200`
`180=((t)/(12))\cdot72`
`(180)/(72)=(t)/(12)`
`2.5=(t)/(12)`
`2.5\cdot12=t`
`30=t`

So the duration of the loan is 30 months.