Question

Michelle borrows a total of $2500 in student loans from two lenders. One charges 4.2% simple interest and the other charges 6.8% simple interest. She is not required to pay off the principal or interest for 3 yr. However, at the end of 3yr, she will owe a total of $354 for the interest from both loans. How much did she borrow from each lender?

Answer 1

Let x represent amount borrowed at 4.2% and y represent amount invested at 6.8%.

We have been given that Michelle borrows a total of $2500 in student loans from two lenders. We can represent this information in an equation as:

$x+y=2500...(1)$

$y=2500-x...(1)$

We are also told that at the end of 3 years, she will owe a total of $354 for the interest from both loans.

Amount of interest earned at a rate of 4.2% in 3 years would be $0.042\cdot 3\cdot x=0.126x$.

Amount of interest earned at a rate of 6.8% in 3 years would be $0.068\cdot 3\cdot y=0.204y$.

We can represent this information in an equation as:

$0.126x+0.204y=354...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.126x+0.204(2500-x)=354$

$0.126x+510-0.204x=354$

$-0.078x+510=354$

$-0.078x+510-510=354-510$

$-0.078x=-156$

$\frac{-0.078x}{-0.078}=\frac{-156}{-0.078}$

$x=2000$

Therefore, Michelle borrowed $2000 at 4.2%.

Upon substituting $x=2000$ in equation (1), we will get:

$y=2500-2000=500$

Therefore, Michelle borrowed $500 at 6.8%.

Answer 2

She borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.

Since Michelle borrows a total of $ 2500 in student loans from two lenders, and one charges 4.2% simple interest and the other charges 6.8% simple interest, and she is not required to pay off the principal or interest for 3 yr, but at the end of 3yr, she will owe a total of $ 354 for the interest from both loans, to determine how much did she borrow from each lender, the following calculation must be performed:

• 4.2 x 3 = 12.6
• 6.8 x 3 = 20.4
• 2500 x 0.126 + 0 x 0.204 = 315
• 2000 x 0.126 + 500 x 0.204 = 354

Therefore, she borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.

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