Question

You are considering a 30 year mortgage offer for a $300K, which has a stated rate of 3.9% APR. Once you consider all the fees, the fee-included APR is 4.12%. What is total of the fees that the lender is charging you? Hint: find the present value of the promised payments at the all-in APR, the difference from face value of 300K is the fees.

Answer 1

Fees charged		=	loan amount-Present value of annuity of monthly paymnet 4.12%
Loan amount		=	Present value of annuity of monthly payment @3.9%
Present value of annuity			=	P[1-(1+r)-n]/r
		where
		p	=	monthly payment
		r	=	3.9%/12=0.325% or 0.00325
		t	=	30*12=360 momths
	Loan amount		=	$300,000
	therfore
		$300,000	=	Monthly payment[1-(1+0.00325)^-360]/0.00325
		$300,000	=	monthly payment [1-(1.00325)^-360]/0.00325
		$300,000	=	monthly payment [1-1.00325^-360]/0.00325
		$300,000	=	monthly payment [1-0.3109]/0.00325
		$300,000	=	monthly payment [0.6890]/0.00325
		$300,000	=	monthly payment 212.013
	$300000/212.013		=	Monthly payment
	$1,415		=	Monthly payment
Present value of annuity of monthly payment @ 4.12%
		monthly payment		=	$1,415
			Rate	=	4.12%/12=0.3433% or 0.003433
			time	=	12*30=360 months
	Present value of annuity			=	1415*[{1-(1+0.003433)^-360}/0.003433]
				=	1415*[{1-(1.003433)^-360}/0.003433]
				=	1415*[{1-1.003433^-360}/0.003433]
				=	1415*[{1-0.2912}/0.003433]
				=	1415*[{0.7088}/0.003433]
				=	1415*206.46
				=	292140.9
	Fees charged		=	$300,000-$292140.9
			=	$ 7,859.10
	There amy little difference due to decimalplaces
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