Based on the details Elena shared with you regarding the potential house sale, please identify the capital gain that would be recognized if she sells the house for $$800,000$ in one month. Please show your calculations and explain your answer.

Elena $($age $68)$ and her husband Joe began working with you five years ago. Unfortunately, Joe died $18$ months ago, after a short illness. You have determined that between Elena$$s IRA, her Social Security income and Joe$$s survivor pension income she should be able to live comfortably into her late $90$s$.$ She updated her will after Joe$$s death, dividing her estate equally between David and Olivia $($her son and daughter$).$ When you met shortly after Joe$$s death, you recommended that she wait a year or so before making any major decisions such as moving.

Elena worked as a human resource professional before retiring at age $65.$ She rolled her $401($k$)$ balance into an IRA when she retired.

She lives in a common law state.

You are scheduled to meet with her in a week. Today, you received the following email from Elena:

Hi $----$

Thanks for your email earlier this week. Lunch after our meeting sounds wonderful.

I thought I$$d give you $$heads up$$ about some of the things I$$d like to talk about. First, I want to thank you for your advice last year about waiting a while to make any big decisions. Things have settled down and I have a better idea of what I want to do$.$

$1.$ I$$d like to sell the house and move into a townhouse a mile or so from the grandkids. I watch them after school so this would be convenient, plus, I$$d love to escape the maintenance of a house. Joe and I bought this house $($jointly owned$)20$ years ago, so this is a big change for me$.$ Can you give me an idea of the capital gain?

Here$$s what I can tell you $$ let me know if you need any other information:

We bought the house in $2003$ for $$246,000.$ We$$ve done repairs, but no additions, etc.

Our mortgage was originally $$150,000,30$ year term and the rate was $5\mathrm{.}25\%.$ We refinanced three years ago for $$90,000(15-$year term and a rate of $3\mathrm{.}5\%).$ The current balance is $$75,564.$

The last time I thought about the house value was while settling Joe$$s estate. Olivia $($my daughter$)$ filed the estate paperwork, and the house was valued at $$700,000.$ I spoke with a Realtor this week who did a market analysis. She thinks it will sell for $$800,000.$ Her commission is $6\%$ of the selling price.