Question

You have a loan outstanding. It requires making ninenine annual payments of $ 9 comma 000$9,000 each at the end of the next ninenine years. Your bank has offered to restructure the loan so that instead of making the ninenine payments as originally​ agreed, you will make only one final payment in ninenine years. If the interest rate on the loan is 7 %7%​, what final payment will the bank require you to make so that it is indifferent to the two forms of​ payment?

Answer 1

In order to be indifferent, both payment should have same time value at the end of 9 years.
Future Value of annual payments at the end of 9 years						=	Annual Payment * Future value of annuity of 1
						=	$             9,000	*	11.97799
						=	$ 1,07,801.90
Working:
Future value of annuity of 1			=	(((1+i)^n)-1)/i			Where,
			=	(((1+0.07)^9)-1)/0.07			i	7%
			=	11.97799			n	9
Thus,
Instead of annual payment, single payment of $ 1,07,801.90 at the end of 9 years will make indifferent in both situation.