Question

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 af

Algebra foundations
ANSWERED
asked 2021-06-17
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.

Expert Answers (2)

2021-06-19
11
 
Best answer
2021-08-04

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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