Why incur the expense of a mortgage when you have sufficient assets to buy the second home outright?
There is no way to determine how much mortgage your can afford from the information given. Formulae and rules of thumb do not consider individual circumstances which can vary widely from family to family. The real question is how much disposable income do you have after deducting your estimated living expenses in retirement. When you itemize your living expenses don't forget to include the taxes, insurance, maintenance, etc. on the second home.
Next comes the problem of inflation. Your living expenses, including the taxes, insurance, maintenance, etc. on the second home, will increase over time. If some of your $100k/yr income is is not inflation indexed then you need to consider where you will be 20 years from now if your living expenses increase at the rate of inflation and some portion of your income remains fixed. Also remember that taxes must be considered. In particular, if you have significant funds in tax sheltered accounts you may find yourself with much larger tax expenses when you reach age 70 1/2 and the RMD (required minimum distribution) rules require you to withdraw these funds and pay the taxes due.
My favorite tool for doing this analysis is Dr. Lawrence Kotlikoff's Economic Security Planner
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It is comprehensive, easy to use and inexpensive.