Project 9: Buying vs. Renting

Thinking Quantitatively Project 9: Buying vs. Renting

Mortgages and Taxes: Deb and Rusty have just gotten married and wish to buy a home.  They both work in Boston and have a combined income of $90,000.  They found a modest starter house which they are buying for $350,000.

  1. The happy couple plan to use their $40,000 is savings to cover the closing costs the bank will charge them, which are 1% of the amount they borrow from the bank. The rest of the savings will be used as a down payment.  So if they borrow $330,000 using $20,000 for a down payment, the closing costs will be $3,300; but they did not use all of their savings up.  Determine the largest amount they can use for a down payment and still pay the closing costs.
Borrow Down Pmt Closing Costs Savings Left
$330,000 $20,000 $3,300 $16,700
  1. Create a 20 year amortization schedule, giving monthly payments, for the amount they borrowed at a 5% annual interest rate.
  1. Compute the total amount of interest they will pay to the bank over the 20 years.
  1. Deb and Rusty know that buying a house will save them money on taxes because they get to deduct the interest they pay to the bank each year and the property taxes they pay each year. First create a column on a worksheet separate from the amortization schedule, for their Income starting at $90,000 and increasing at 3% for 20 years.
  1. Next create a column for their Property Taxes which are currently $3,100 a year and will also increase by 3% a year.
  1. Create another column for the amount of Interest they paid to the bank each year (careful here, your amortization schedule is monthly).
  1. Create another column for the yearly Deductions = Property taxes + Interest.
  1. Next a column for Taxable Income = Income – Deductions.
  2. Go to www.savewealth.com click on Tax Forms, Income Tax Rates, and then Married Filing Jointly to find the tax formula for Deb and Rusty.  Create a column computing the yearly federal taxes.  Note that Deb and Rusty change tax brackets over the 20 years, so you must change formulas.

Buying versus Renting:

We want to compare the two options of buying the house versus continuing to rent an apartment.

  1. Assume the rent is now $1000 a month and will increase by 3% a year.
  2. Compute their federal income taxes, which are higher when renting because they don’t have the deductions.
  1. By renting they are saving a lot of money each year! They pay less for rent than mortgage, and they don’t pay property taxes (they do however pay more in income tax).  Assume the extra money (include the $40,000 in savings as initial deposit) they have from renting versus buying is all invested at 10% a year, and every year their extra money is added to this account.  How much does this amount to after 20 years?
  1. Assume the house increases in value by 3% a year.
  1. Which option ends up with more money for Deb and Rusty to retire on assuming they sell the house after 20 years?


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