Marisa borrows $4,400 for 6.5 years at a fixed rate of simple interest. At the end of that time she owes $7,500. The annual rate of interest being charged has to be determined.

An amount P, at an annual rate of interest r, in n years earns an interest equal to P*r*n. The total amount, sum of principal, and interest is given by P+P*r*n.

Marisa has borrowed $4,400 initially at a fixed rate of simple interest. Let this rate of interest be r. In 6.5 years, the total amount is equal to

4,400+4,400*r*6.5

= 4400+28600*r.

Equating this to $7,500 gives

4,400+28,600*r = 7,500.

Solving for r,

28,600*r = 7,500-4,400

r = (7,500 - 4,400)/28,600

r = 0.10839.

The annual rate of interest being charged is equal to 10.839%.

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