Suppose you bought a $1 million dollar house with the down payment of 20%. You b

Question

Suppose you bought a $1 million dollar house with the down payment of 20%. You borrowed the remaining 80% with some xed interest rate.

(a) (5 points) What is your equity?

(b) (6 points) Suppose that the price of your house immediately fell by 10%. What is your equity now? Is your mortgage under water?

(c) (6 points) Suppose that instead the price of your house fell by 30%. What is your equity in this case, and are you under water?

(d) (8 points) Suppose instead that the 30% fall in the price occurred after several years of you owning the house during which you repaid 25% of your initial mortgage loan. What is your equity in this case and are you under water? Compare your answer to that in part (c) and explain.

Explanation / Answer

House amount = $1 million

down payment= 20% of $1 million

= 200000

80% remaining amount= 800000

a) the equity is value of house- the mortage loan amount

i.e. $1 million- 800000= 200000

b) If the price of the house fell by 10%. the market value of house is $1 million-(10% of $1 million)

i.e. 900000

The mortgage amount is 800000

Equity= 900000-800000

=100000

The mortgage is not under water.

c) If the price of the house fell by 30%. the market value of house is $1 million-(30% of $1 million)

i.e. 700000

The mortgage amount is 800000

Equity= 700000-800000

=-100000

Yes the mortgage is under water now as the equity is negative.

d) 25% or mortgage amount = 25% of 800000

= 200000

so remaining mortgage amount= 600000

If the price of the house fell by 30%. the market value of house is $1 million-(30% of $1 million)

i.e. 700000

Equity= 700000-600000

=100000

The mortgage is not under water.

In part (c) the equity was negative and the price of house fell immediately but in part (d) the price fell happened after the 25% amount was paid and the equity is not negative.

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