# How do equity, amortization, and market value factor into net profit on a sold house?

TL;DR:

If I buy my first house at \$500k using an FHA loan, and I want to eventually buy a \$1MM home (with a conventional 20%-down loan), how do I calculate the time at which the sale of my first house will result in having \$200k cash-on-hand? Equity, Market growth and Interest vs Principle all factor in here, but I'm not sure how to turn these variables into an equation.

Context:

I'm planning on using a 3.5%-down FHA loan to get into my first house in an area with very rapid price growth.

I understand that once the Loan-To-Value ratio reaches a certain point (~80%), refinancing with a conventional loan would help me avoid the need for Mortgage Insurance. However, I'm also considering that my first house will likely be smaller than what I would prefer and if I can end the initial FHA mortgage loan by selling my first house with enough equity to move to a larger house using a traditional 20-percent-down mortgage, I can kill two birds with one stone by 1) ending the PMI and 2) living in a house that suits my needs.

Because of the nature of the typical mortgage amortization, I know that I will be paying mostly interest at first. This seems to imply that it will be easier to refinance the home once the LTV reaches a certain point, and at a later point it will be possible to sell the home and end up with enough cash-on-hand to make a 20% payment down on a more expensive home.

The easiest way to get a handle on this will be in a spreadsheet. You can easily build an amortization table in Excel or copy one from an online amortization calculator. Then add your property value estimate next to the amortization schedule and compare the ending balance from each month with the estimated property value to get estimated equity for each month. Divide that estimated equity value by the target cost of a new house for each month and find the month where your equity hits 20% of the desired new house cost.

Remember to add the 1.75% MIP to the purchase price after deducting your down payment for actual loan amount.

I whipped up this in just a few minutes after the refresher on the `PMT()` function found in the linked video, you could make it nicer in not much time:

In my sample, at 5% interest and 7% annual home value growth you'd have enough equity for a 20% down payment on a million dollar house right around 4 years after purchasing current house.

Note that the payment you calculate when following the video linked will be lower than your actual payment amount since it doesn't include monthly MIP or property taxes in escrow, but those don't affect the equity calculations.

Edit: To be more realistic, the growth rate of the new property should be estimated as well, since it will likely change in value as well. Even if the two grow at the same rate, you'd want to calculate the growth of both rather than exclude growth from the equation.

• "but those don't affect the equity calculations" - Wow that's great, and make this a lot easier. Thanks for the demo table. Feb 4, 2018 at 1:34
• Exactly what I was thinking, but wasn't at desktop computer. +1 and will delete my answer. Nice work. Feb 4, 2018 at 2:48
• Can we really count on property value to increase by 10% per year ? Why not just keep the house for 10 years and you'll have a \$1M home that you bought for 500k. Feb 5, 2018 at 20:20
• @xyious I estimated 7% growth, which I certainly wouldn't count on, but assuming no growth is pretty unrealistic as well. The exercise of estimating growth helps with making some decisions about if it's worth re-financing when they hit 20% equity of current home to get away from MIP or just waiting until they hit 20% of the more expensive home. Feb 5, 2018 at 21:41
• @xyious That's a good point and I updated my answer. I disagree with your conclusion since the same growth rate on different starting values don't cancel out, so rather than growth being moot the growth of both houses should be estimated. For example, if we set growth in my example to 0% then it will take ~206 months for equity to hit 20% of the new property vs 69 months if both properties increase at 7%. Feb 5, 2018 at 22:37