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Liam borrowed a total of $35,000 to pay for college. he pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. what average interest rate does he pay on the total $35,000? (round your answer to the nearest tenth of a percent.)

Respuesta :

Answer: Liam pays an average interest of 5.9% on the total $35,000.

Since the amounts borrowed and the respective interest rates are different, the weighted average will give us a better picture of the average interest paid on the loan.

We calculate weights based on the total amount borrowed.

                             Borrowing ($)                  Weights

Parents                     3000            [tex]\frac{3000}{35000}[/tex] = 0.228571429

Bank                       32000           [tex]\frac{32000}{35000}[/tex] = 0.771428571

Total                       35000                                                                     1

Once we have the weights, we multiply the interest rates with the respective weights. Then we find the total of the (weights * Interest rate) column to find the weighted average or the average rate Liam pays.

                      Weights       Int Rates        Weights * Interest rates

Parents       0.228571429      0.03  [tex]0.228571429*0.03 = 0.006857143[/tex]

Bank           0.771428571       0.068[tex]0.771428571 *0.068 = 0.006857143[/tex]

Total                       1                                          0.059314286

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