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Maria took out an unsubsidized Stafford loan of $6,925 to pay for college. She plans to graduate in 4 years. The loan had a duration of ten years and an interest rate of 5.0%, compounded monthly. By the time Maria graduates, how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization? Round all dollar values to the nearest cent.

 Apr 14, 2014
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Maria took out an unsubsidized Stafford loan of $6,925 to pay for college. She plans to graduate in 4 years. The loan had a duration of ten years and an interest rate of 5.0%, compounded monthly. By the time Maria graduates, how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization? Round all dollar values to the nearest cent.

Interesting question.  Let me see if I can get my head aroundwhat you are asking.  

I don't know what the 10 years has to do with anything so I will ignore it.

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Interest only monthly repayments would be

I=Prt  where P=$6925,  r=0.05/12 t=1  

I=6925*0.05/12 = $28.854166666  (Oh, I didn't round to nearest cent, you can do that)

She will have to pay this every month for 4 years 4*12=48months

$28.854166666*48= $1385

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If she doesn't pay anything towards the loan then after 4 years she will owe S=P(1+r)n   

S=6925*(1+0.05/12)48     

S=$8454.70 (to the nearest cent)

Interest part is 8454.70 - 6925 = $1529.70

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so if she pays the interest monthly she will save herself

1529.70 - 1385.00 = $144.70

I think this is what you are being asked for.  

 Apr 15, 2014

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