I've got 60k and I'm looking at buying a house for 145k. The bank offered me a 20 year loan of 100k at ~1.8% interest rate. After 20 years I would have repaid the bank around 16k, according to their loan offer.
I'm looking to calculate the equivalent return-of-investment per year I'd need to have if I wanted to make the same amount of money with a different investment, assuming I keep the house for X years and then sell it. The initial numbers don't matter too much, I'm more interested in the calculation.
I've seen several related questions but haven't found one that shows this calculation directly. Please excuse me if it's a duplicate.
Here's what I've got:
Buying the house costs around 160k (145k + 15k for closing costs). Property values typically go up ~2% a year. So at year X the house is worth 145*(1.02^X).
The rent from the house covers the loan, property taxes and regular maintenance, with a negligable amount left over. So after X years, I would have paid back 116*X/20 of the loan, therefore I'd have 116*(1-X/20) of it left to pay. That means after paying back the loan, I have
145*(1.02^X) - 116*(1-X/20)
left. My initial investment was 60k, so I'd have
[145*(1.02)^X - 116*(1-X/20)]/60
times my initial investment. Assuming I want the same behavior from another investment (compounded yearly), I'd need
{[145*(1.02)^X - 116*(1-X/20)]/60 } ^ (1/X)
roi per year. I get these values for X = 5, 10, 15 and 20 years:
X = 5 => 1.04 => 4% yearly ROI
x = 10 => 1.07 => 7% yearly ROI
x = 15 => 1.07 => 7% yearly ROI
x = 20 => 1.066 => 6.6% yearly ROI
Is this calculation correct? What does it leave out that should be considered?
Edit: replaced "notary fees" with "closing costs" as per Ben Voigt's comment