Question

Find the values requested in the problems. Round all answers to 2 decimals and please identify the parts for your responses

You decide after a few successful years in the field, you decided that it's time to buy a house. you speak to the bank and the take out mortgage for $175,000 for 30 years ( that is the price of a home today is $175,000)

a) IF YOU PAY 1% PER MONTH WHAT IS YOUR MONTHLY PAYMENT

b) Assume housing prices appreciate 4% per year. What will the approximate value of your home be at the end of the mortgage?

c) How would your payments change if you took a 15 year mortgage and paid 2% per month?

d) would this change the future value of your home in 30 years? if so, to what?

Answer 1

Answer to (a)

Monthly Payment is calculated by the below formulae

=(P x R x (1+R)^N)/((1+R)^N-1)

Where P = $ 175 000 , R = 1% per month = 0.01 and

N = Total number of monthly payments for 30 years = 12x30 =360

Putting the formulae, we get

Monthly Payment = (175000x0.01x(1+0.01)^360)/((1+0.01)^360-1)

=(1750 (1.01)^360) / ((1.01)^360 -1)

=(1750 x 35.95)/ (35.95-1)

=62912.50/ 34.95

=1800.07

So, Monthly Payment = $1800.07 for 1% per month interest payment for 30 year mortgage

b) With 4% appreciation in prices , approximate value of home at the end of mortgage ( 30 years)

is calculated by the formulae = P (1+ r/n) ^nt

Where P = $175000 , r = 4% = 0.04 , n= number of times interest applied per time period =1

and t = number of time periods = 30 years

Then, Approximate Value of home = 175000( 1+0.04/1) ^ 1*30

= 175000(1+0.04) ^ 30

= 175000 (1.04) ^ 30

= 175000 (3.2434)

= 567595

So , Approximate value of home with 4% appreciation every year at the end of mortgage = $567595

c) Computation of monthly payment with 15 year mortgage and paid 2% per month

So then using the above formulae , here the values are

P = 175000 , R = 2% per month = 0.02

N = Total number of monthly payments for 15 years = 12 x 15 = 180

Now , Applying the above formulae

Monthly Payment =(P x R x (1+R)^N)/((1+R)^N-1)

= ( 175000 *0.02( 1+0.02) ^ 180) / (1+0.02) ^ 180 -1)

= (3500 (1.02) ^ 180) / ((1.02 ) ^ 180 -1)

= (3500 x 35.32 ) / ( 35.32 -1)

=  123 620 / 34.32

= 3601.98

Monthly payment with 2% per month interest rate for 15 years mortgage = $ 3601.98

d) Future value of home will certainly change in 30 years . It depends at what rate appreciation happens.

Like at a appreciation of 4%, future value of home after 30 years  = $567595 ( As calculated above)

Interest rate had some effect on the value of house. When the interest rate is low , then there is high demand for home and prices of home rises and on the reverse when the interest rate is high , then prices of home decreases.

Total payment for 30 years with 1% per month = 1800.07 x 30 x 12= $648025.2

Total payment for 15 years with 2% per month = 3601.98 x 15 x 12 =$648356.4

So, there is lttle extra payment with 2% per month = 648356.4 - 648025.2 = $331.2