You are looking to take out a 300K USD mortgage for 30 years. After shopping aro

Question

You are looking to take out a 300K USD mortgage for 30 years. After shopping around, you have two offers on the table:

Bank 1: 2.9% interest rate, up front fees of 3,984 USD
Bank 2: 3.59% interest rate, up front fees of 3,031 USD

Notice the tradeoff between the rate and the fees: you can pay a higher up front fee in exchange for a lower interest rate.

How long (at a minimum) must you anticipate staying in this house, in order for the loan from Bank 1 to be better for you? (To make this ballpark estimate, ignore time value of money for simplicity.)

Hint: find the difference between the monthly payments for the two mortgages. See how long it takes to 'make up' for the extra up front fee on the lower-rate loan.

Explanation / Answer

1) PV = 200000

let x be monthly installment

x * [1 - (1+0.069/12)^-360]/0.069/12 = 200000

x = 1317.20

2)
PV = 1382 * [1 - (1+0.075/12)^-360]/0.075/12

= 197650.36

3)

for bank 1

PV = 300000

let x be monthly installment

x * [1 - (1+0.029/12)^-360]/0.029/12 = 300000

x = 1248.69

for bank 2

PV = 300000

let x be monthly installment

x * [1 - (1+0.0359/12)^-360]/0.0359/12 = 300000

x = 1362.25

extra upfront fee = (3984 - 3031) = 953

difference between monthly payments = 113.56

minimum no of months must stay = 953/113.56 = 8 .39 = 8 months

or take 9 months

upto you

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