Question

a. Prepare the amortization schedule for a thirty-year variable interest loan with monthly payments of $250,000 at an APR of 6.8%. specifies monthly compounding.

b.What is the interest payment and principal amounts in the 110th payment?
c. Use the annuity formula to find how much principal you still owe to the bank for the 110th payment. Check that this value is the same you have in your amortization schedule.

d. How much in total interest will you pay?

e. Suppose that in the beginning of the first month of the fourth year the interest rate increased to 7.8%. Modify the amortization schedule in order to consider this change in the interest rate (you should change the values in your schedule that occur after the first month of the fourth year, not the ones before this date). 7.8% in the last line.

f. Suppose that in beginning of the first month of the fourth year (month 37) you can refinance your mortgage at the rate of 6.8%. Assume that there is no change in the time scheduled to pay the mortgage. If the cost of refinancing is $2,750, should your refinance your mortgage at the new rate of %, or keep the rate of 7.8%?

g. Suppose that at the end of the seventh year you earned an unexpected amount of money (for example from your end of year bonus at work) and decided to pay a non-scheduled payment of $8,000 of the principal of the loan. You will keep paying the same monthly total payment that you were paying in the previous months. How can you change your amortization schedule, considering that you will keep paying the same total monthly amount? Prepare a new amortization schedule that accounts for these changes.

Answer 1

	Pmt	Monthly payment	$250,000
	Rate	Monthly interest=(6.8/12)%	0.005666667
	Nper	Number of months of payment	360	(30*12)
		Amount of Loan =Present value of future payments
	PV	Amount of Loan	$38,347,958	(Using PV function of excel with Rate=0.00566667,Nper=360, Pmt=-250000)
	b)	Principal amount balance after 110 th payment	$33,375,317
		Interest amount paid in 110 months:
		Total amount paid=110*250000=	$27,500,000
		Total Principal Paid=38347958-33375317	$4,972,641
		Total interest paid=27500000-4972641=	$22,527,359
	c)	Future Value of 110 payments:
		Compound Amount Factor (CAF):
		(((1+i)^N)-1)/i
		i=interest rate=0.005666667
		N=number of months=110
		CAF=(((1+0.005666667)^110)-1)/0.005666667	152.092247
		Future Value of 110 payments=CAF*250000	$38,023,063
		Future Value of Loan=	$71,398,380
		Loan balance after 110 payment	$33,375,317
	d	Total amount paid in 30 years	$90,000,000	(250000*360)
		Loan amount	$38,347,958
		Total Interest paid=90000000-38347958=	$51,652,042
		AMORTIZATION SCHEDULE
				A	B	C=A*0.005666667	D=B-C	E=A-D
			Month	Beginning Balance	Monthly Payment	Interest	Principal	Ending Balance
			1	$38,347,958	$250,000	$217,305	$32,695	$38,315,264
			2	$38,315,264	$250,000	$217,120	$32,880	$38,282,383
			3	$38,282,383	$250,000	$216,934	$33,066	$38,249,317
			4	$38,249,317	$250,000	$216,746	$33,254	$38,216,063
			5	$38,216,063	$250,000	$216,558	$33,442	$38,182,621
			6	$38,182,621	$250,000	$216,368	$33,632	$38,148,989
			7	$38,148,989	$250,000	$216,178	$33,822	$38,115,166
			8	$38,115,166	$250,000	$215,986	$34,014	$38,081,152
			9	$38,081,152	$250,000	$215,793	$34,207	$38,046,946
			10	$38,046,946	$250,000	$215,599	$34,401	$38,012,545
			11	$38,012,545	$250,000	$215,404	$34,596	$37,977,949
			12	$37,977,949	$250,000	$215,208	$34,792	$37,943,158