A homeowner can obtain a $250,000, 30-year fixed-rate mortgage at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.25 points. How long must the owner stay in the house to make it worthwhile to pay the payment saving is invested monthly?

Break even point  = 5.90 years

Explanation:

given data

loan amount = $250,000

time N = 30 year = 360 months

rate I/y = 6 % =  6% / 12

rate I/y = 5.5 %  = 5.5% / 12

solution

we get here PMT for both Loan rate 5.5% and 6% is

for loan A

PMT( monthly rate, time period, loan amount )

PMT( 6/12  , 360 , -$250,000 )

PMT = $1498.88    1

and for loan B

PMT( monthly rate, time period, loan amount )

PMT( 5.5/12  , 360 , -$250,000 )

PMT = $1,419.47     2

so here saving is

Savings = Loan A – Loan B

Savings = $1498.88 - $1,419.47  

Savings = $79.40

Point will be  = $250000 × 2.25%

points = $5625

so here Break even point will be

Break even point  = points ÷ savings   3

Break even point  = 5625 ÷ 79.40

Break even point  =70.84 month

Break even point  = 70.84 ÷ 12

Break even point  = 5.90 years

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