Loan Interest. Sharon is considering the purchase of a car. After making the down payment, she will finance $11,450.00. Sharon is offered 3 maturities. On a four-year loan she will pay $284.93 per month. On a five-year loan, Sharon’s monthly payment will be $237.68. On a six-year loan they will be $206.39. Sharon rejects the four-year loan, as it is not within her budget. How much interest will Sharon pay over the life of the five-year loan? Of the six-year loan? Which should she choose if she bases her decision solely on interest paid?

Hi, in order to find the amount of interest that Shannon would have to pay for each of the loans, she has to multiply the annuities (payments) of each of the loans for the months until she pays, in the case of the 5 year loan (60 months) and in the case of the 6 year loan (72 months). After that, she has to substract the price of the car from the result found in each case, that is as follows.

In the case of the 5 year loan.

[tex]Interest=237.68*60-11,450=14,260.80-11,450=2,810.80[/tex]

So, she pays $2,810.80 in interest for the 5 year loan.

Now, let´s see how much would she pay if she chooses the 6 year loan.

[tex]Interest=206.39*72-11,450=14,860.08-11,450=3,410.08[/tex]

If she chooses to get the 6 year loan, she would have to pay $3,410.80 in interest.

Therefore, if she bases her decision solely on the interest paid for each loan, she would choose the 5 year loand, since she would have to pay less interest.

Best of luck.