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# Applied Math 40S Slides May 10, 2007

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Home buying? renting? A Case Study.

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### Applied Math 40S Slides May 10, 2007

1. 1. Rent or Buy? A Case Study ... The Browns have an opportunity to buy a home valued at \$50 000 with a down payment of \$5000 and a mortgage of \$45 000, or rent the home for \$525 per month. If they buy, they will get a 15-year mortgage at 7.5%. Annual property taxes are approximately 1.5% of the market value (i.e. the sale price) of the home. They expect their home to appreciate in value by about 2% per year. (That is, it will become 2% MORE VALUABLE each year. If it is worth \$100 this year, next year it will be worth \$102 and the year after that it would be worth \$104.04.) If they rent, their rental payments will increase by 3% each year, and they expect to get a 7% annual return on their investment of the \$5000 they did not use as a down payment.
2. 2. (a) What is the size of the monthly mortgage payment?
3. 3. (b) What will their equity be in the home after two years of ownership?
4. 4. (c) After one year, how does the cost of payments plus property taxes compare with the cost of rental payments?
5. 5. (d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments?
6. 6. (d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments?
7. 7. (d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments? (e) What might be some reasons for the Brown family to rent instead of buy - even though renting seems to be more expensive in the long run? (f) What is the net cost of owning the home for 10 years? Of renting for 10 years?