Question

Your local lender offers you a fixed-rate mortgage with the following terms: $220,000 at 5.50% for 30 years, monthly payments. The lender will charge you two discount points and the loan has a 4% prepayment penalty.
A. (1 pt) What is the annual percentage rate (APR) of the loan?
B. (1 pt) How many points are required to yield an APR of 5.75%?

Answer 1

A.

Loan Amount = $220000

term = 30 years = 360 month

interest rate = 5.50% per annum or 0.4583% per month

Initial charges = $220000*2% = $4400.

We hve to find the Monthly payment for the loan.

=>Monthly payment = $1249.14.

Annual percentage rate of the loan or APR is the effective rate to the Borrower.

Current Cash inflow to the buyer = $220000-$4400= $215600

Monthly cash outflow = $1249.14.

Present value (PV)	$215,600	Excel Formula
Total period(n)	360
PMT or payment	$1,249.14
Rate per Month	0.4737%	=Rate(360,-1249.14,215600,0,0,)
		RATE(number_of_periods, payment_per_period, present_value, [future_value], [end_or_beginning], [rate_guess])
APR (Rate per month*12)	5.684%

henec,

annual percentage rate (APR) of the loan = 5.684%.

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Answer-B

Current Cash inflow to the buyer=????

APR = 5.75 % per year OR 0.479167 %per month

Monthly cash outflow = $1249.14.

Total period(n)	360
PMT or payment	$1,249.14
APR	5.75%
Rate per Month	0.479167%	(5.75%/12)
Present value or Present cash flow(A)	$214,050.30	=PV(0.479167%,360,-1249.14,0,0)
		=PV(rate, number_of_periods, payment_amount, [future_value], [end_or_beginning])
Total Loan value(B)	$220,000
initial charges(B-A)(C)	$5,950
Discount point (C/B*100)	2.704%

2.704% DISCOUNT POINT REQUIRED TO YIELD AN APR OF 5.75%