SOLUTION: A loan of 17400 dollars is to be repaid in annual installments of 2100 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A loan of 17400 dollars is to be repaid in annual installments of 2100 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1192592: A loan of 17400 dollars is to be repaid in annual installments of 2100 dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is 8.2 percent, what is the outstanding balance owed immediately after the 5th payment?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you are given the effective rate interest per year of 8.2%.
the loan amount is 17400.
the payments at the end of each year are 2100.
with 2100 being paid at the end of each year, it will take 14.43513668 years to satisfy the loan.
the amount owed immediately after the 5th payment will be equal to 13434.83269.
this is equal to 13434.83 when rounded to the nearest penny.

i used the texas instruments BA-II-Plus calculator to get these results.

there is an online calculator at https://arachnoid.com/finance/index.html that will give you comparable results.

here are the displays from using that calculator.

the first two displays show the inputs and output for finding the number of years required to satisfy the loan.
you provide all the inputs for everything except np (number of time periods) and then you click on np to get the number of years required to satisfy the loan.

the second two displays show the inputs and output for find the balance remaining immediately after making the 5th payment.
the output from the first two displays tells you that the number of years to satisfy the loan is equal to 14.44.

to find the remaining balance after the payment at the end of the fifth year, you subtract 5 from 14.44 to get 9.44.
you input number of years at 9.44 and then solve for present value to get the remaining balance of the loan.

here are the displays.









i also used excel to show you the year by year transactions.
that is shown below.


you can see that the remaining balance at the end of year 5 is equal to 13434.82369.

the ti-ba-ii calculator and excel agree.
the online calculator doesn't agree.
this is because the online calculator rounded the number of years to 2 decimal places, affecting the result.