Question

Queenie just bought a house that cost $1,600,000. She has saved up $200,000 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 4% (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 75% of the purchase price of the house or the appraised value, whichever is lower. The appraised value of the house is $1,400,000. The estimated closing costs (legal fees etc.) are $20,000.

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

Answer (a):

Purchase price of the house = $1,600,000

Appraised value of the house is = $1,400,000.

Bank can lend only up to 75% of the purchase price of the house or the appraised value, whichever is lower.

Maximum amount that the bank will lend her = 75% * 1400000 = $1,050,000

Maximum amount that the bank will lend her = $1,050,000

Answer (b):

Period = 25 * 12 = 300

Loan amount = 1050000

Effective annual rate = (1 + 4%/2)^2 - 1 = 4.04%

Monthly interest rate = (1 + 4.04%)^(1/12) -1 =0.3305890%

Monthly payment to the bank = PMT(rate, nper, pv, fv, type) = PMT(0.3305890%, 300, -1050000, 0, 0)

= $5523.21

Monthly payment to the bank = $5,523.21

Answer (c):

Money she needs to close the purchase = Purchase cost + Closing cost - Maximum amount that bank would lend

= 1600000 + 20000 - 1050000

= $570,000

Money she needs to close the purchase = $570,000

Answer (d):

Saving amount she has = $200,000

Money she needs to close the purchase = $570,000

Second mortgage loan amount = 570000 - 200000 = $370,000

Period = 20 * 12 = 240 months

Effective annual rate = (1 + 10%/2)^2 -1 = 10.25%

Monthly interest rate = (1 + 10.25%)^(1/12)-1 =0.8164846%

Monthly payment = PMT(rate, nper, pv, fv, type) = PMT(0.8164846%, 240, -370000, 0,0) = $3521.1584

Mothly payment = $3,521.16

Answer (e):

Outstanding balance after two years on the private mortgage = Present value of remaining monthly installnets

Remaining months = 240 - 24 = 216 months

Outstanding balance after two years on the private mortgage = PV (rate, nper, pmt, fv, type)

= PV(0.8164846%, 216, -3521.1584, 0, 0)

= 356798.43

Outstanding balance after two years on the private mortgage = $356,798.43