Question

Michelle borrows a total of $6000 in student loans from two lenders. One charges 4.4% simple interest and the other charges 6.3% simple interest. She is not required to pay off the principal or interest for 4 yr. However, at the end of 4 yr, she will owe a total of $1246 for the interest from both loans. How much did she borrow from each lender? Part 1 out of 2 Michelle borrowed S at 4.4%

Answer 1

Let the amount of loan Michelle borrowed from lender 1 be x dollars and the amount of loan Michelle borrowed from lender 2 be y dollars.

Total amuount of loan = $6000

x + y = 6000 ......(1)

Lender 1 charges 4.4% simple interest and lender 2 charges 6.3% for 4 years. Total interest after 4 years is $1246.

Simple Interest = (Principal x rate x time)/100

$\small \frac{x\times 4.4\times 4}{100}+\frac{y\times 6.3\times 4}{100}=1246$

$\small \frac{x\times 4.4}{100}+\frac{y\times 6.3}{100}=311.5$

2 x 4.4+ y x 6.3 = 31150

$\small 44x+63y=311500$ ...........(2)

From eq.(1),

y = 6000 - x

44x + 63(6000 - x) = 311500

44x + 378000 - 63x = 311500

44x - 63x = 311500 - 378000

-19x = -66500

x = 3500

y = 6000 - 3500

y = 2500

Michelle borrowed $3500 at 4.4%, and

Michelle borrowed $2500 at 6.3%.

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