Question

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?

Answer 1

Answer:

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