Question

Queenie just bought a house that cost $2,600,000. She has saved up $400,000 for the closing costs--such as legal fees—and the down payment. When she approaches the local bank, she was quoted the rate for a two-year mortgage at 5% (APR, semi-annual compounding), 25 years amortization. But there is one problem; she was told that her income satisfied the bank’s GDS and TDS requirements, but the bank can lend only up to 70% of the purchase price of the house or the appraised value, whichever is lower. The appraised value of the house is $2,400,000. The estimated closing costs (legal fees etc.) are $40,000.

1. What is the maximum amount that the bank will lend her?
2. What is the monthly payment to the bank?
3. How much money does she need to close the purchase?
4. To close the purchase, she plans to get a second mortgage from a private lender. The rate for a two-year term second mortgage is quoted at 10% (APR) with semi-annual compounding, and amortization period of 20 years. What is the monthly payment?
5. What is the outstanding balance after two years on the private mortgage?

Answer 1

Part (a):

Maximum loan= 70% of cost or appraised value whichever is lower.

Appraised value is lower at $2,400,000.

Hence maximum loan= $2,400,000*70% = $1,680,000.

Part (b):

5% APR semi annual compounding is equal to 4.948699% nominal rate with monthly compounding as follows:

Monthly payment= $ 9,770.96 as follows:

Part (c):

Total cost= $2,600,000. Loan amount= $1,680,000.

Therefore, down payment= $2,600,000-$1,680,000 = $920,000

Closing costs= $40,000.

Therefore, total amount needed to close the purchase= $920,000 + $40,000 = $960,000.

Part (d):

Amount needed as per part (c )= $960,000

Amount of savings available= $400,000.

Therefore, private mortgage availed= $960,000 - $400,000 = $560,000.

10% APR semi annual compounding is equal to 9.797815% nominal rate with monthly compounding as follows:

Monthly payment= $ 5,329.32 as follows:

Part (e):

Outstanding balance in the private mortgage after 2 years= $540,019.25

Relevant portion of amortization schedule as below: