Finding how much the loan is and borrowed

Question

Your loan payment is $276.25 every month and the loan is for 5 years with an annual percentage rate of 4%. How much did you borrow? Justify in detail how you arrived at your answer.

Answer 1

Since the loan is for 5 years, that is a total of 60 payments .... (12 monthly payments, for 5 years ... 5*12 = 60)

 

The total amount of money paid (including interest) = 60 * 276.25 = 16575

 

The formula for simple interest is I = Prt, where 

     I = interest

     P = principal amount borrowed

     r = interest rate (decimal) ... 4% = .04 as a decimal number

     t = time, in years ... 5

 

Since the total amount paid back (16575) includes the principal and the interest,

   

    Let "p" equal the principal amount borrowed

    

    The interest expense for 5 years can be computed using ... I = Prt

        I = Prt  

        I = p(.04)(5)

        I = 0.2(p)

 

    The amount repaid ... minus the interest charged ... equals the amount borrowed

    

         16,575 - 0.2p = p

         16,575 = p + .2p

         16,575 = 1.2p

         16,575/1.2 = 1.2p/1.2

 

         $13,812.50 = p

 

         The original amount borrowed is $13,812.50