You are considering whether to buy or rent a residence. You think you'll probably move in the next 8 years, so that's your time horizon for this decision.

If you buy, the place costs $100K. You have to pay 20K as a downpayment, and take out a mortgage for the rest. Your mortgage payment will be fixed at $452. Additionally, you have to cough up 3K for various mortgage-associated fees at the start. Additionally, you'll need to pay $200 in property taxes every month, an amount that will grow with inflation. Additionally, you'll need to buy home insurance in the amount of $90 every month, an amount that will also grow with inflation. Assume the value of your house will also grow with inflation. At the end, when you sell your house, you'll have to pay a commission in the amount of 6% of sales price to the real estate broker. To save yourself some calculations, assume the outstanding mortgage balance at time of sale is $65K. Assume you will also need to spend on average 1/12 of 2% of home value in various maintenance expenses, per month, an amount that will grow with inflation.

If you rent, your initial monthly rent will be in the amount of $767, an amount that will grow with inflation. You will also need to put down an extra payment in the same amount at the start, as a security deposit. Assume you get it back at the end. You will also need to buy renter's insurance, which will cost $15 per month, an amount that will grow with inflation.

Assume inflation will be about 2% APR. Assume the relevant discount is 6% APR. Assume all payments happen at the end of the month, to keep things simple.

Under these conditions, what is the net benefit to you of buying the home?

Hint: find the present value of all the purchase-associated cash flows, and subtract the present value of all the rent-associated cash flows. Pay attention to the signs!