Question

You are purchasing a new home and need to borrow $325,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.5% APR for a 30-year fixed-rate mortgage (with payments made at the end of each month). The mortgage lender also tells you that if you are willing to pay one point, they can offer you a lower rate of 6.25% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $3,250 to cover points you are paying the lender. Assume that you do not intend to prepay your mortgage (pay off your mortgage early).

a) The monthly interest rate of the 6.5% APR mortgage loan is %？

B）the monthly payment of the mortgage loan

C) The monthly interest rate of the 6.25% APR mortgage loan is % ？

D) Assume the cost of the capital of the lending bank is 5% (effective rate). From the bank's perspective, the monthly cost of capital is—— %？, and the net present value (NPV) of lending the 6.5% APR loan is $——？

Answer 1

formulas used :-

	loan value	325000
	interest rate	0.065
	reduced rate	0.0625
A)	monthly rate	=D5/12
C)	reduced monthly rate	=D6/12
	tenure (in months)	360
B)	monthly payment	=PMT(D7,D9,-D4)
D)	monthly cost of capital	=5%/12
	NPV	=PV(D11,D9,-D10)-D4