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what is the maximum amount ginger Logan can borrow today if it must be repaid in 23 months with simple interest at 6% and she knows that at the time she will be able to repay no more than $23,000?(round to the nearest dollar as needed)

Respuesta :

Answer:

$20,628

Explanation:

The amount that Logan will repay can be calculated as:

[tex]A=P(1+rt)_{}[/tex]

Where P is the amount that she will borrow, r is the annual rate and t is the time in years.

So, we can replace A by 23000, r by 6%, and t by 23/12 because a year has 12 months. Then:

[tex]23000=P(1+(0.06\cdot\frac{23}{12}))[/tex]

Finally, to know the maximum amount that Logan can borrow, we need to solve the equation for P as:

[tex]\begin{gathered} 23000=P(1+0.115) \\ 23000=P\cdot1.115 \\ \frac{23000}{1.115}=P_{}_{} \\ 20628=P \end{gathered}[/tex]

So, the answer is $20,628

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