Question

You want to buy your dream house. You currently have $15,000 saved and you need to have a 10% down payment plus an additional 5% of the loan amount for closing costs. The price of the house is $1,005,879. You can earn 7.5% per year in a savings account per year. How long will it be before you have enough money for the down payment and closing costs? __________________

Given your current credit, you secure a 15-year fixed rate mortgage at 3.12%. Calculate your monthly mortgage payment; you must pay the home loan on the 1st of each month. Payment: ___________________

Now, consider the possibility of being able to make one additional mortgage payment per year for each of the 15 years. How much will you save in interest payments? ________________

Answer 1

Lets understand the given information:

• House cost is $1,005,879
• Down payment = 10% of cost
  • Down payment = 0.10 x 1,005,879 = 100587.90
• Loan amount = Cost - down payment
  • Loan amount = 1005879 - 100587.90
  • Loan amount = 1005879 - 100587.90
  • Loan amount = 905291.10
• We need to have the down payment and 5% of loan amount
  • FV = 100587.90+0.05 x 905291.10
  • FV = 145852.50
• We need to find the time it will take for 15000 to grow to 145852.50 @ 7.5% p.a.
  • We are given the following information

  • PV	15000
    r	7.50%
    frequency	1
    FV	$        1,45,852.50

  • We need to solve the following equation to arrive at the required n
  • 
  • 
  • 
  • So it will take 31.45 years to accumulate the amount required.
• Now lets calculate the mortgage payment:
  • First we need to understand that the payment on 1st of each month starts one month from the date of loan
  • We are given the following information:

  • r	3.12%
    n	15
    frequency	12
    PV	$   9,05,291.10

  • We need to solve the following equation to arrive at the required PMT
  • 
  • 
  • PMT = 6304.15
  • So the monthly payment will be 6304.15
  • Following is the amortization schedule:
  • 
• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Loan-Principal repayment
• PMT is calculated as per the above formula
• Interest = 0.0312 /12 x opening balance
• Principal repayment = PMT - Interest

Now we need to keep the PMT same and make every 12th payment double the original amount to accommodate one additional payment per year. This leads to loan being paid off by 164th month

Total interest paid previously was  $2,29,456.64 while now we pay only 207653.25 so the savings is the difference of the two, which = $21,803.39