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suter [353]
2 years ago
8

After four years in college, Josie owes $21000 in student loans. The interest rate on the federal loans is 3% and the rate on th

e private bank loans is 4.4%. The total interest she owes for one year was $714.00.What is the amount of each loan?
Mathematics
1 answer:
klasskru [66]2 years ago
7 0

Answer:

$104.27 is the amount at 3% and $20895.73  is the amount at 4.4%

Step-by-step explanation:

We are given that Josie owes $21000 in student loans.

Let x be principal at 3% rate of interest

Time = 1 year

Formula:A=P(1+r)^t

A=x(1+0.03)^1

A=1.03x

Interest = Amount - Principal

Interest = 1.03x-x=0.03x

So, (21000-x) is the principal at 4.4% rate of interest

Formula:A=P(1+r)^t

A=(21000-x)(1+\frac{4.4}{100})^1

A=21924-1.044x

Interest = 21924-1.044x-21000-x=924-2.044x

The total interest she owes for one year was $714.00

So, 0.03x+924-2.044x=714

x=104.27

So, $104.27 is the amount at 3%

The principal at 4.4% rate of interest =21000-x=21000-104.27=20895.73

Hence $104.27 is the amount at 3% and $20895.73  is the amount at 4.4%

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