Assume today is January 1st, 2010. You purchased a house and took a mortgage 10
year ago (January 1st 1,2000). The house price was $500,000 when your purchased it. Your
mortgage was written with interest rate 6% (nominal annual interest rate) and was to be
repaid by 30 years with equal monthly payment. The mortgage is due on the end of each
month (i.e. your first payment was due on January 31st, 2000).
a) Find out monthly payment level.
b) Assume that, in the last year, due to economic recession you were laid off and missed
the last 6 payments (the most recent missed payment was due on Dec 31, 2009). Find out
the current outstanding balance of your mortgage. How much principle have you paid so
far?
c) Due to government assistant program, your house is not foreclosed and there is no
penalty for the missed payment. But you have to pay off your loan in original time (i.e.,
in 20 years from now) with equal monthly payment. Find out the monthly payment level
(You monthly payment level is changed because you missed 6 payments and interest of 6
missed payments).
d) Assume that, after you pay one year from now(12 payments), you can refinance your
mortgage with very lower interest rate 3% due to the new assistant program. Find out
your monthly payment level if you refinance your mortgage.
Answers & Comments
Verified answer
Washi -
It is more work than hard, simply manipulating a bunch of annuity formulas:
a) Find out monthly payment level.
500000 = P[1-(1+.06/12)^(-12*30)] / (.06/12)
P = $2997.75
b. Current outstanding balance
Current Balance =
500000(1+.06/12)^(12*10) - {$2997.75[(1+.06/12)^(12*10 - 6) - 1]/(.06/12)}(1.005^6)
Current Balance = 436641.89
Principal Paid So Far = 500000 - 436641.89 = 63358.11
c) 436641.89 = P[1-(1+.06/12)^(-12*20)] / (.06/12)
P = 3128.24
d) Balance 12 months from now:
436641.89(1.005)^12 - 3128.24(1.005^12 - 1)/.005
Balance = 424984.41
New Payment: 424984.41 = P[1-(1+.03/12)^(-12*19)] / (.03/12)
P = 2447.66
Hope that helps