You have a loan outstanding. It requires making ninenine annual payments of $ 9 comma 000$9,000...

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?

Expert Solution

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.

jeff jeffy answered 1 year ago

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