You said that you figured the interest you will have paid over the first 3 years will be the same with the 15- and the 30-year mortgages. That is not quite accurate.
Let's look at the numbers.
From the monthly payment numbers you gave, it looks like you were figuring on a 4.0% rate. That seems quite high, as the current national average mortgage rates are currently 2.86% for a 15-year fixed rate and 3.61% for a 30-year fixed rate. Since you are planning on selling in 3 years, you could potentially get an even better rate by getting an adjustable rate mortgage; the current national average for a 5-year adjustable rate is 2.80%. However, rates can vary locally and with your credit situation, so I'll assume that 4.0% is the best rate you can get for either a 15-year or 30-year mortgage. (If you can get a lower rate, you could save quite a bit, even in only 3 years.)
For a $230K, 15-year mortgage at 4.0%, over the next three years, here is what you would pay:
- Monthly payment: $1,701.28 ($61,246.08 over 36 months)
- Total interest paid in first 36 months: $25,561.08
- Remaining principal after first 36 months: $194,314.92
- Equity in house, assuming no change in value: $35,685.08
If, instead, you went with the 30-year mortgage at 4.0%, here is what you are looking at:
- Monthly payment: $1098.06 ($39,530.16 over 36 months)
- Total interest paid in first 36 months: $26,877.06
- Remaining principal after first 36 months: $217,347.07
- Equity in house, assuming no change in value: $12,652.93
So the difference in interest paid between the two options in the first three years is a little over $1,300.
Because of the larger payment, the difference in equity after 3 years is much greater: over $23,000. The reason this is important is that, with only 3 years between the time you buy the house and the time you sell it, there is no guarantee that the value of the house will go up in that time. The value could just as easily be less three years from now. With the 30-year mortgage, you are only putting in $13k toward your principal, and if the value of the home drops, you could find yourself upside-down in the mortgage. With the 15-year mortgage, you would be putting in over $35k toward your principal, and could withstand a much larger drop in value before you find yourself underwater.
Having said that, the difference in equity between the 15- and 30-year mortgages is offset by the amount you save in payment each month. Therefore, if you hold on to your extra $600 per month you don't have to pay with the 30-year, your difference between the two options is only the $1,300 interest. If you spend the $600 per month, you could find yourself in trouble.
As for your rental option, there are a few things missing from your comparison:
If you buy, you will need to pay property tax. As a renter, the property taxes are included in the rent.
If you buy, you will need to pay homeowners insurance. As a renter, you only need much less-expensive renters insurance.
If you buy, you are at risk for a downturn in the housing market when you want to sell. As a renter, you simply walk away after 3 years.
If you buy, you are on the hook for any maintenance costs that come up, from a leaky faucet to a leaky roof. As a renter, the landlord is responsible.
Selling a house every 3 years generally means that you will be paying various closing costs (realtor commission, appraisal, title insurance, etc.) every 3 years. This will eat away at any equity you would be gaining in the mortgage. If you are renting, this is not a concern.