Question

The Taylors have purchased a $320,000 house. They made an initial down payment of $20,000 and secured a mortgage with interest charged at the rate of 6%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.) $ Incorrect: Your answer is incorrect. What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)

Answer 1

Since the Taylors paid an initial amount of $20000, the loan amount is:
320,000-20,000=$300,000.
We need to compute the value of the amount that the Taylors have to pay 
after 30 years with 6% interest rate like this:
300,000(1+6%)^(30)=$1723047
In order to find the amount that has to be paid each month, divide the previous amount over 30 years like this:
$\frac{1723047}{30}=57434 \text{ dollars each month}$

Answer 2

Part A: monthly payment

Initial loan after downpayment,  
P = 320000-20000= 300,000

Interest rate per month, 
i = 0.06/12= 0.005

Number of periods, 
n = 30*12= 360

Monthly payment, 
A = P*(i*(1+i)^n)/((1+i)^n-1)
= 300000(0.005(1.005)^360)/(1.005^360-1)
= 1798.65


Part B: Equities
Equity after y years
E(y) = what they have paid after deduction of interest
= Future value of monthly payments - cumulated interest of net loan
= A((1+i)^y-1)/i - P((1+i)^y-1)
= 1798.65(1.005^y-1)/.005 - 300000(1.005^y-1)
= (1798.65/.005-300000)(1.005^y-1)

Equity E
for y = 5 years = 60 months
    E(60) = (1798.65/.005-300000)(1.005^60-1) = 18846.17
for y = 10 years = 120 months
    E(120) = (1798.65/.005-300000)(1.005^120-1) = 45036.91
y = 20 years = 240 months
    E(240) = (1798.65/.005-300000)(1.005^240-1) = 132016.53

Check: equity after 30 years
y = 30 years = 360 months
    E(360) = (1798.65/.005-300000)(1.005^360-1) = 300000.00  .... correct.