Question

There are two related questions in this mortgage problem. Must respond to both. Suppose you are buying a house that costs $400,000. You put 25% as down payment and the rest you get 15-year mortgage at 4.6% with your 35^th Bank.
i. What is your ending balance at the end of year two.
ii. Suppose you are planning to pay off the remaining debt as “balloon payment at the end of year 10 with 1.5% prepayment penalty. How much money do you need to pay to 35^th Bank to own your house completely at the end of year 10?

Answer 1

Answer (i):

Cost of house = $400,000

Down payment = 400000 * 25% = $100,000

Loan amount = PV = 400000 - 100000 = $300,000

NPER in months = 15 * 12 = 180 months

Monthly interest = RATE = 4.6%/12

Monthly payment = PMT (rate, nper, pv, fv, type)

= PMT (4.6%/12, 180, -300000, 0, 0)

= $2310.34178

Ending balance at the end of year two = PV of remaining monthly installments

Remaining NPER = 180 - 2*12 = 156

PV of remaining monthly installments = PV(rate, nper, pmt, fv, type)

= PV(4.6%/12, 156, -2310.34178, 0, 0)

= $270,888.94

Ending balance at the end of year two = $270,888.94

Answer (ii):

Ending balance at the end of year 10 = PV of remaining monthly installments

Remaining NPER = 180 - 10*12 = 60

PV of remaining monthly installments = PV(rate, nper, pmt, fv, type)

= PV(4.6%/12, 60, -2310.34178, 0, 0)

= $123623.55

Ending balance at the end of year 10 = $123,623.55

Prepayment penalty = 1.5%

Money do you need to pay to bank = 123623.55 +123623.55 *1.5% = $125,477.90

Money do you need to pay to bank at the end of Year 10 = $125,477.90