SOLUTION: Debtor borrows $6000. Pays, at the end of each year for 12 years, $500 of the principal and simple interest at 4% on all principal left unpaid during the year. Find the total money

Algebra ->  Finance -> SOLUTION: Debtor borrows $6000. Pays, at the end of each year for 12 years, $500 of the principal and simple interest at 4% on all principal left unpaid during the year. Find the total money      Log On


   

Question 1165092: Debtor borrows $6000. Pays, at the end of each year for 12 years, $500 of the principal and simple interest at 4% on all principal left unpaid during the year. Find the total money paid by the debtor in dicharching his debt.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i used the TI-BA-II financial calculator to solve this.
my inputs were:
present value = 0
future value = 0
interest rate per year = 4%
number of years = 12
payments are made at the end of each year.

the calculator told me that the payments that needed to be made at the end of each year are equal to $639.31 rounded to the nearest penny.

the sum of the payments is equal to 7671.76 rounded to the nearest penny.

subtract the amount of the loan to get the total interest paid.
that would be the sum of the payments minus 6000 = 1671.76 rounded to the nearest penny.

each payment is divided between interest and equity.
the interest is calculated from the remaining balance of the loan.
the equity is the payment amount minus the interest amount.

the percent of the payment that is interest (increases the remaining balance of the loan) is largest at the beginning of the loan and smallest at the end of the loan.

the percent of the payment that is equity (reduces the remaining balance of the loan) is smallest at the beginning of the loan and largest at the end of the loan.

i did the year by year calculations in excel to show you what i mean.

that is shown below:



a typical end of year calculation is shown below.

remaining balance at end of year 3 = 4753.50
interest on this remaining balance at the end of year 3 is 190.14 (shown at the end of year 4)
payment on the remaining balance at the end of year 3 is 639.21 (shown at the end of year 4)
remaining balance at the end of year 4 = 4304.33.
this is equal to the remaining balance at the end of year 3 plus the interest on the remaining balance at the end of year 3 minus the payment.
the equity portion of the loan is the payment minus the interest portion of the loan.
that is equal to 449.17