Question 14 0/1 pts You\'re planning to buy a house in the current price r of $2

Question

Question 14 0/1 pts You're planning to buy a house in the current price r of $200,000. The price of houses in this price range is increasing at 2% per year. If you put 10% down ($20,000 now) you can get a 30 year fixed rate loan at 5% APR compounded monthly. If you put 0% down, you can get a 30 year fixed rate loan at 3%. You have enough how to make 10% down payment, but won't have enough for a 20% down payment until next year. Your savings account earns 5% APR compounded monthly. How much will you save in present value terms by waiting one year and putting down the larger down payment? Round your answer to the nearest dollar Do not include $ sign or commas. (E.e., 12345) swered

Explanation / Answer

Case 1.

Downpayment=10% of house cost =10%*$200000=20000

Loan value=$180000

Interest rate=5% compounded monthly

Time=30 years=360 months

Monthly mortgage payment= $966.28 (calculated as per month mortage using above parameters)

Case 2

Downpayment=20% of house cost

New house cost=1.02*200000=204000 (2% increase from previous year)

Downpayment=$40800

Loan value=$163200

Interest rate=3% compounded monthly

Time=30 years=360 months

Monthly mortgage payment= $688.06

PV of payments under case 1 discounted at 5% monthly rate=$180000

PV of payments under case 2 discounted at 5% monthly rate=$128172 (PV at year 1 end)

PV pf payment under case 2 at year 1 beginning=$121934

Saving =180000-121934=$58066

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