Eric borrowed a total of $4000 from two student loans. One loan charged 5% simple interest and the other charged 4.5% simple interest, both payable after graduation. If the interest he owed after 3 years was$547.50, determine the amount of principal for each loan.

Question
Algebra foundations
Eric borrowed a total of $4000 from two student loans. One loan charged 5% simple interest and the other charged 4.5% simple interest, both payable after graduation. If the interest he owed after 3 years was$547.50, determine the amount of principal for each loan.

2020-10-29
If x is invested at 5%, then 4000−x is invested at 4.5%.
The simple interest earned in 3 years is $547.50 so each year, the simple interest earned is$547.50/3=182.50 so we can write:
$$\displaystyle{0.05}{x}+{0.045}{\left({4000}−{x}\right)}={182.50}$$
Solve for x:
$$\displaystyle{0.05}{x}+{180}−{0.045}{x}={182.50}$$
$$\displaystyle{0.005}{x}={2.50}$$
$$\displaystyle{x}=\frac{{2.50}}{{0.005}}$$
$$\displaystyle{x}={500}$$
So, the Eric loaned $500 at 5% and$3,500 at 4.5%.

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