Algebra World Problem

Question

The annual interest rate paid for a $12000 simple interest loan was $240 less than the interest paid on a $25000 loan at 1.5% less interest per year. What was the total interest paid on the $25000 loan for one year? (all rounding should be to 3 decimal places). For credit you must show all work.

Answer 1

For simple interest there is no compounding so...

 

The first statement says: interest rate paid for a $12000 simple interest loan was $240 less than the interest paid on a $25000

 

Translation:

eq1. 12,000*i = y_i - 240

 

where i is the interest rate and y_i is the total interest per year

 

The second statement:interest paid on a $25000 loan at 1.5% less interest per year

 

Translation:

eq2. 25,000*(i-.015) = y_i

 

 

Now we can rearrange to have y_i be on the same side.

 

eq1. 12,240*i = y_i

eq2. 25,000*i-375 = y_i

 

set two equations equal to each other:

 

12,240*i = 25,000*i-375 

 

now solve for i

 

12,760*i = 375

 

i = 375/12,760

i = 0.29  - rounded

 

This represents the interest rate paid by the 12,000 loan. Now to find the interest rate paid by the larger loan, simply plug in the rate to eq2.

 

25,000*(.029-.015) = y_i

 

y_i = 350