Financail Markets A bank offers a home buyer two options for mortgage payment: O
ID: 2734657 • Letter: F
Question
Financail Markets A bank offers a home buyer two options for mortgage payment: Option 1: $1.48 million loan, 30-year fixed-rate mortgage at a rate of 6.01 percent with zero points. Option 2: $1.48 million loan, 30-year fixed-rate mortgage at a rate of 5.5 percent with 2.12 points. If you will keep the mortgage for 30 years, what is the net present value of the monthly savings(or costs) of paying the points? Hint: net present value of the savings is the present value of savings minus the points paid up front.
Explanation / Answer
Formula for monthly Mortgage payment
P = [ R / (1- (1 +R)^-N)] * loan amount
Where:
P is the constant payment for every month= ?
R is the interest rate per year = 6.01% and 5.5% or 6.01/12 = 0.50% and 5.5/12 = 0.46% per month
N is the number of years = 30 0r 30*12 = 360 months
Loan is the total loan amount = $ 1.48 Million
Option 1,
P = [0.005/ (1- (1+0.005)^-360)] *$ 1.48 million
= $8,873.35
Option 2,
P = [0.0046/ (1- (1+0.0046)^-360)] *$ 1.48 million
= $8,421.86
And upfront payment in option 2 = $ 1.48* 2.12% = $31,376
Difference in the monthly payment in option 1 and option 2 = $ 8,873.35 - $ 8,421.86 = $ 451.49
Different amount of $ 451.49 is the monthly saving for 360 months so to calculate the present value of this difference we can assume it like an annuity payment and formula for present value of an annuity is
PV = P * [ (1- (1+R)^-N) /R]
Where
P is the constant amount for every month = $ 451.49
R is the interest rate per year = 5.5% or 5.5/12 = 0.46% per month
N is the number of years = 30 0r 30*12 = 360 months
Now PV = $ 451.49 * [(1- (1+0.0046)^-360) / 0.0046]= $ 79,341.78
The net present value of the monthly savings = the present value of savings - the points paid up front
= $ 79,341.78 - $ 31,376 = $ 47,965.78
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