Joanie takes a \(\$6000\) loan to pay for her car. The annual interest rate on the loan is \(12\%\). She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest compounds annually? Express your answer as a dollar value to the nearest cent.

jxc516 Mar 21, 2021

#1**0 **

Compound annually ==> 9441.12

Compound quarterly ==> 9563.09

Difference = 121.97

Guest Mar 21, 2021

#2**+2 **

Joanie takes a 6000 dollar loan to pay for her car. The annual interest rate on the loan is 12percent . She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest compounds annually? Express your answer as a dollar value to the nearest cent.

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Compounded annually it will become 6000(1+0.12)^4 = 9441.11 dollars, which means the interest component is 441.11 dollars

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4 years is 4*4=16 quarters, and 12% per year (nominal) is 12/4 = 3% per quarter

So 6000 dollars will grow to 6000(1+0.03)^16 = 9628.24 dollars (to the nearest cent)

so that will be 3628.24 dollars interest

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You can finish it :)

I had to get rid of the dollar signs because the program thought it was latex and it didn't print properly.

Melody Mar 22, 2021