Question

You have a loan outstanding. It requires making six annual payments of $ 6 comma 000 each at the end of the next six years. Your bank has offered to restructure the loan so that instead of making the six payments as originally​ agreed, you will make only one final payment in six years. If the interest rate on the loan is 7 %​, what final payment will the bank require you to make so that it is indifferent to the two forms of​ payment?

Answer 1

Answer: The final payment would be: $42919,74.

Explanation: To simplify the work we must make a timeline:

0            1               2             3           4              5               6

        $6000      $6000     $6000    $6000    $6000       $6000

These would be the normal conditions of the loan.

but if instead of making the 6 payments only one is made at the end:

We must use the FV annuity formula:

6000 × $\frac{(1+0,07)^{6} - 1 }{0,07}$ = 42919,74