1
$\begingroup$

A loan of $17,000$ dollars is to be repaid in annual installments of $2,100$ dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is $8.8$ percent, what is the outstanding balance owed immediately after the $5th$ payment?

Im pretty confused on how to go about solving this, I know that outstanding balance is equal to the payment amount times the present value at a specified time, but I am confused how to go about setting up the equation properly.

$\endgroup$
6
  • $\begingroup$ I dont´know, if I understand the exercise right. It is payed back $\$2,100$ five times, is that right ? What does "...followed by a final smaller payment." mean in this context ? $\endgroup$
    – callculus42
    Nov 3, 2015 at 3:01
  • $\begingroup$ i think it means that after the final payment (5th payment is not the final payment) a smaller payment is made (ie. >2100) $\endgroup$
    – user286414
    Nov 3, 2015 at 3:05
  • $\begingroup$ Therefore we only have to consider the five payments of 2,100 dollars each, right ? $\endgroup$
    – callculus42
    Nov 3, 2015 at 3:07
  • $\begingroup$ correct id assume, but maybe you must factor in the final smaller payment to determine the number of payments needed in order to calculate outstanding balance? $\endgroup$
    – user286414
    Nov 3, 2015 at 3:17
  • $\begingroup$ no i dont, but i know 14 000 is incorrect since when i input it in webwork it comes up as incorrect. It is the last problem in this set and I'm absolutely stumped.. $\endgroup$
    – user286414
    Nov 3, 2015 at 3:20

1 Answer 1

Reset to default
0
$\begingroup$

The future value of the loan after 5 years is $17,000\cdot(1.088)^5$.

The future value of the 5 payments is

$C_5=2100\cdot (1.088)^4+2100\cdot (1.088)^3+2100\cdot (1.088)^2+2100\cdot (1.088)^1+2100\cdot (1.088)^0$

  • The first payment has to be compounded 4 times.

  • The last payment has not be compounded.

$2100\cdot \left[ (1.088)^4+ (1.088)^3+ (1.088)^2+2100\cdot (1.088)^1+ (1.088)^0 \right]$

The expression in the brackets is the partial sum of a geometric series. Therefore

$C_5=17,000\cdot(1.088)^5-2100\cdot \frac{1-1.088^5}{1-1.088}$

I hope it helps.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .