Question

Marie and Alex just paid $250,000 for a house. They made a down payment of $50,000 and assumed a 30-year $200,000 mortgage with a fixed annual interest rate of 5.50%. The house will serve as a residence for several years, but Marie and Alex also view it as an investment, as property values in the neighborhood are projected to increase at a rate of 5% per year in the near future. Property taxes on their home will be $4,236 the first year and are expected to increase 3% a year. Homeowners insurance will cost $632 the first year and is expected to increase at a rate of 2% each year.  The couple plans to sell the house after eight years. Answer the following questions.

1. What is their monthly payment on principle and interest?  Do not include property taxes or home owners insurance (AKA. escrow payment).

2. What would the couple pay in monthly payments over the 8 years that they owned the house?

Answer 1

Value of house	250000
Less: Down payment	50000
Mortgage amt.	200000
No.of months of mortgage payment(30 yrs.*12)=	360
Annual interest rate	5.50%
Monthly interest(5.50%/12)	0.4583%

1. Their monthly payment on principle and interest

can be calculated using the formula to find the present value of ordinary annuity

ie. PVOA=Pmt.*(1-(1+r)^-n)/r

where,

PVOA= present value of the mortgage , ie. $ 200000

Pmt.--- is the monthly pmt.--to be found out---??

r= the monthly rate of interest, ie. 0.4583% as found out above

n= no.of monthly pmts., ie. 360

Now, plugging -in all the values in the formula,

ie.200000=Pmt.*(1-(1+0.4583%)^-360)/0.4583%

so, the monthly pmt.=200000/(1-(1+0.4583%)^-360)/0.4583%)=

1135.53

(Answer)

2.Monthly payments over the 8 years that they owned the house
Year	1	2	3	4	5	6	7	8
Monthly payment on mortgage (principle and interest)	1135.53	1135.53	1135.53	1135.53	1135.53	1135.53	1135.53	1135.53
Property taxes(4236/12), increasing at 3% per year	353	363.59	374.50	385.73	397.30	409.22	421.50	434.15
Homeowner's insurance(632/12), increasing at 2% per year	52.67	53.72	54.79	55.89	57.01	58.15	59.31	60.50
Monthly expenses in all the 8 yrs.	1541.20	1552.84	1564.82	1577.15	1589.84	1602.90	1616.34	1630.17