Question

Problem 4 and 5-7 House Appreciation and Mortgage Payments Say that you purchase a house for $320,000 by getting a mortgage for $280,000 and paying a $40.000 down payment you get a 30 year mortgage with an interest rate of 8 percent, what are the monthly payments (Do not round Intermediate calculations and round your final answer to 2 decimal places.) sont What would the loan balance be in ten years? (Round the payment amount to the nearest cent but do not round any other interim calculations. Round your final answer to 2 decimal places.) Loan balance If the house appreciates at 4 percent per year, what will be the value of the house in ten years? (Do not round Intermediate calculations and round your final answer to 2 decimal places.) Future value How much of this value is your equity? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Equity

Answer 1

1.

Here we know the present value of the mortgage loan that is $280,000.

We also know that Present Value of Future Annuity (PVFA) is:

PVFA = A (1 + i/a)na - 1 i/a(1 + i/a na

Where,

A = Annuity or monthly payments

i = rate of interest

a = number of payments in a year

n = number of years

So, let us put the values in the formula;

280000 = A (1 + 0.08/12)30-12 - 1 0.08(1 + 0.08/12)30-12

280000 = A 9.93572965775562 0.0729048643850375

280000 136.283494133963

- 2054.54

The monthly payments are $2,054.54 each.

2.

Balance in 10 years.

By the end of the 10^th year we would have made 120 payments (10*12).

Remaining balance of loan after 10 years:

= PV(1 + i/a)na - A (1 + i/a)na - 1 i/a

Where,

PV = original balance at the beginning

A = payments

na = number of payments made

"a" and "i" are same as above equation.

= 280000(1 + 0.08/12) 120 _20545a (1 +0.08/12) 120 -1 0.0812

= 280000(2.21964023454471)-2054.54(182.946035181707)

= 245629,32

Therefore, the loan balance at the end of 10 years =$245,629.32

3.

Appreciation of house:

Here, we need to find the future value (FV) of house appreciated at 4% per year for 10 years.

FV = P(1 + i)"

Where, i = rate of appreciation

n = number of years

FV = 320000(1 + 0.04.16

= 320000(1.48024428491834)

=47368.17

Therefore, the value of house after 10 years appreciated at 4% per year =$473,678.17

4.

In that your equity will be (at year 10)

= Value of house - Loan payment remaining

=$473,678.17 - $245,629.32

= $228,048.85