You plan to purchase a house for $250,000 using a 15-year mortgage obtained from

Question

You plan to purchase a house for $250,000 using a 15-year mortgage obtained from your local bank. You will make a down payment of 25% of the purchase price. Your bank offers you Ihc following 2 options for payments: Mortgage rate of 6.25% and 1.3 points Mortgage rate of 5.50% and 2.6 points. Suppose you are expecting a big inheritance in 10 years; therefore, you are planning to pay off the entire remaining balance on the 10^th anniversary of your purchase. Which option should you choose? Payments are made monthly. Show detailed calculations

Explanation / Answer

Option 1 :

Purchase Price = 250000

Down Payment = 25% * 250000 = 62500

Loan required = 250000-62500 = 187500

Processing Charges = 1.3 point i.e 1.3%

Loan to be taken = Loan required/(1-Processing Charges )

Loan to be taken = 187500/(1-1.3%)

Loan to be taken = 189,969.60

Monthly Payment = pmt(rate,nper,pv,fv)

rate = 6.25%/12

nper = 15*12 = 180

pv = -189969.60

fv = 0

Monthly Payment = pmt(6.25%/12,180,-189969.60,0)

Monthly Payment = $ 1628.84

Balance Outstanding at the end of 10 year = pv(rate,nper,pmt,fv)

rate = 6.25%/12

nper = (15-10)*12 = 60

pmt = 1628.84

fv = 0

Balance Outstanding at the end of 10 year = pv(6.25%/12,60,1628.84,0)

Balance Outstanding at the end of 10 year = $ 83,748.17

Effective Monthly interest rate = rate(nper,pmt,pv,fv)

nper = 10*12 =120

pmt = 1628.84

pv = 187500

fv = 83748.17

Effective Monthly interest rate = rate(120,1628.84,-187500,83748.17)

Effective Monthly interest rate = 0.5397%

Option 2 :

Purchase Price = 250000

Down Payment = 25% * 250000 = 62500

Loan required = 250000-62500 = 187500

Processing Charges = 2.6 point i.e 2.6%

Loan to be taken = Loan required/(1-Processing Charges )

Loan to be taken = 187500/(1-2.6%)

Loan to be taken = 192,505.13

Monthly Payment = pmt(rate,nper,pv,fv)

rate = 5.5%/12

nper = 15*12 = 180

pv = -192505.13

fv = 0

Monthly Payment = pmt(5.5%/12,180,-192505.13,0)

Monthly Payment = $ 1572.93

Balance Outstanding at the end of 10 year = pv(rate,nper,pmt,fv)

rate =5.5%/12

nper = (15-10)*12 = 60

pmt = 1572.93

fv = 0

Balance Outstanding at the end of 10 year = pv(5.5%/12,60,1572.93,0)

Balance Outstanding at the end of 10 year = $ 82,347.35

Effective Monthly interest rate = rate(nper,pmt,pv,fv)

nper = 10*12 =120

pmt = 1572.93

pv = 187500

fv = 82347.35

Effective Monthly interest rate = rate(120,1572.93,-187500,82347.35)

Effective Monthly interest rate = 0.4957%

Decision : Option 2 Should be selected as its monthy payment is lower and Effective Monthly interest rate is lower than option 1

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