Question

You are planning on taking a loan for $ 49 ,000. You will repay the loan in annual payments over the next 7 years and the loan has a stated interest rate of 6 %. For the very last payment on your loan, how much of this is repayment of principal? For example, if the loan payment is $400 of which $30 is interest and $370 is principal, your answer is $370. Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

Answer 1

Step-1:Calculation of Monthly Payment
	Annual Payment		=	Loan Amount/ Present Value of annuity of 1
			=	$       49,000	/	5.5823814
			=	$   8,777.62
	Working:
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i		Where,
				=	(1-(1+0.06)^-7)/0.06		i	6%
				=	5.5823814		n	7
Step-2:Preparation of Loan Amortization Schedule
	Year	Beginning Loan amount			Interest Expense		Annual Payment		Reduction in Principal			Ending Loan Balance
	1	$ 49,000.00			$ 2,940.00		$ 8,777.62		$ 5,837.62			$ 43,162.38
	2	$ 43,162.38			$ 2,589.74		$ 8,777.62		$ 6,187.87			$ 36,974.51
	3	$ 36,974.51			$ 2,218.47		$ 8,777.62		$ 6,559.15			$ 30,415.37
	4	$ 30,415.37			$ 1,824.92		$ 8,777.62		$ 6,952.69			$ 23,462.67
	5	$ 23,462.67			$ 1,407.76		$ 8,777.62		$ 7,369.86			$ 16,092.82
	6	$ 16,092.82			$     965.57		$ 8,777.62		$ 7,812.05			$   8,280.77
	7	$   8,280.77			$     496.85		$ 8,777.62		$ 8,280.77			$            0.00
Thus,
	Repayment of Last payment in the form of Principal					$ 8,280.77