When you buy a house, you need to choose the type of loan. The options available
ID: 2716206 • Letter: W
Question
When you buy a house, you need to choose the type of loan. The options available to you are: A: 30year fixed rate of 4% per year interest, 5% down B: 15year fixed rate of 3.5% per year interest, 15% down Other information: Price of house is $150,000 House will be sold after 10 years for $170,000 Taxes and insurance (T&I) are $300 per month Amount available: maximum of $40,000 for down payment, $1600 per month, including T&I New loan expenses: origination fee of 1%, appraisal fee $300, survey fee $200, attorney’s fee $500, processing fee $350, escrow fees $150, other costs $300. Any money not spent on the down payment or monthly payment will earn taxfree interest of ¼% per month. a. Calculate the future worth at the end of a 10yr period. b. Which loan should you choose?
Explanation / Answer
Assuming origination fee on total amount of 150000.
Future worth
Option A
Down payment = 5% or 7500.00
Loan exp = 1% of 150000 + (300+200+500+350+150+300) = 3300.00
amount left = 29200.00
Value at 10 year end at .25 pm or 3% pa montly compounding = 39401.00
monthly interest = 4/12 = 0.33%
emi = 685.00 every month for 30 years
money save from monthly alowance = 1600 - 300 - 685 = 715.00
pricipal outstanding at the end of 10 yrs = 113055.00
FV of money saved from monthly allowance , calculated at annuity of 715 per month for 10 years or 120 months at .25% per month i.e. 3% per annum
= 100126
Money at 10th year = House sale + deposit amount + balance from down payment - loan repayment
= 170000 + 100126 + 39401 - 113055 = 196472.00
Option B
Down payment = 15% or 22500.00
Loan exp = 1% of 150000 + (300+200+500+350+150+300) = 3300.00
amount left = 14200.00
Value at 10 year end at .25 pm or 3% pa montly compounding = 19,160.00
emi = 911.00 every month for 30 years
money save from monthly alowance = 1600 - 300 - 911 = 389.00
pricipal outstanding at the end of 10 yrs = 50104.00
FV of money saved from monthly allowance , calculated at annuity of 389 per month for 10 years or 120 months at .25% per month i.e. 3% per annum
= 54,474.00
Money at 10th year = House sale + deposit amount + montly savings - loan repayment
= 170000 + 19160 + 54474 - 50104 = 193530.00
Money at 10th year is higher under option A hence i would choose Option A loan.
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