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According to the future value concept, the lender stand to lose in the absence of PMI is $352,696
Future value
Future value means the implied value of an asset as of a specific date in the future based upon a growth rate assumption.
Given,
Suppose you are thinking about purchasing a small office building for $1,500,000. The 30 year fixed rate mortgage that you have arranged covers 80% of the purchase price and has an interest rate of 8%. Assume you were to default and go into foreclosure in year 10 of this loan
Here we need to find the amount that the lender stand to lose in the absence of PMI if the selling price is $700, 000
In order to find the solution we need to do the following steps,
Mortgage amount = 80% * 1,500,000 = 1,200,000
Interest rate = 8% i.e. (8%/12)
Monthly Term = 30 years which equal 360 months
Now, by using the formula of FV,
1,200,000 = Monthly Payment * ((1-(1-0.08))³⁰
When we simplify it then we get the value of land as $352,696.
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