The Taylors have purchased a $290,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 10%/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 Taylor's be required to make?
How do I find out what is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years?
amount to be mortgaged = .9(290000)
= 261,000
i = .10/12 = .008333... (keep as is in calculator memory)
n = 30(12) = 360
payment = p
p( 1 - 1.008333..^-360)/.008333 = 261000
I get p = $2290.46
I will do the "outstanding balance" after 5 years, you do the other two cases in the same way.
Amount of debt if no payments had been made
= 261000(1.0083333...)^60
= 429,425.62
value of 60 payments
= 2290.46(1.008333..^60 - 1)/.008333..
= 177366.65
outstanding debt = 429,425.62 - 177366.65
= 252,058.98
Check with your notes , text, or instructions
how you are to calculate "equity".
I am not in the US, so am not familiar with your methods.
To find out the monthly payment required to amortize the mortgage over 30 years, we can use the formula for a fixed-rate mortgage:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount (initial house price - down payment)
r = monthly interest rate (annual interest rate / 12)
n = total number of monthly payments (30 years * 12)
Let's calculate the monthly payment first:
P = $290,000 - $10,000 = $280,000
r = 10% / 12 = 0.00833
n = 30 * 12 = 360
M = $280,000 * 0.00833 * (1 + 0.00833)^360 / ((1 + 0.00833)^360 - 1)
Calculating this equation gives us the monthly payment amount for the Taylors.
Now, to find their equity after 5 years, 10 years, and 20 years, we need to consider the principal amount paid off by those times. Since the mortgage is amortized, every monthly payment includes both principal and interest.
To determine the principal amount paid off after a specific period, we can use the loan amortization formula. Assuming the monthly payment is constant over time, we can calculate the remaining principal balance using the following formula:
B = P * ((1 + r)^n - (1 + r)^t) / ((1 + r)^n - 1)
Where:
B = remaining principal balance after time t
P = principal loan amount (initial house price - down payment)
r = monthly interest rate (annual interest rate / 12)
n = total number of monthly payments (30 years * 12)
t = number of monthly payments made
To find the equity, subtract the remaining principal balance from the initial house price.
Let's calculate the equity for each time period mentioned:
1. After 5 years:
t = 5 * 12 = 60 months
B = $280,000 * ((1 + 0.00833)^360 - (1 + 0.00833)^60) / ((1 + 0.00833)^360 - 1)
Equity = $290,000 - B
2. After 10 years:
t = 10 * 12 = 120 months
B = $280,000 * ((1 + 0.00833)^360 - (1 + 0.00833)^120) / ((1 + 0.00833)^360 - 1)
Equity = $290,000 - B
3. After 20 years:
t = 20 * 12 = 240 months
B = $280,000 * ((1 + 0.00833)^360 - (1 + 0.00833)^240) / ((1 + 0.00833)^360 - 1)
Equity = $290,000 - B
By plugging in the values for each case, the respective equities can be calculated.
To find out the Taylors' equity after a specific number of years, you need to calculate how much of the mortgage they have paid off over that period.
First, let's calculate the monthly payment they need to make to amortize the loan over 30 years.
Using the formula for the monthly payment on an amortizing mortgage:
M = P * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount
r = Monthly interest rate
n = Total number of payments
Given:
P = $290,000 - $10,000 (down payment) = $280,000
r = 10% per year / 12 months = 0.008333 (approx.)
n = 30 years * 12 months = 360 months
Plugging these values into the formula:
M = $280,000 * (0.008333 * (1+0.008333)^360) / ((1+0.008333)^360 - 1)
Using a calculator, the monthly payment is approximately $2,332.71.
After calculating the monthly payment, you can determine the equity after a specific number of years by subtracting the remaining unpaid balance from the original loan amount.
To find the unpaid balance after a particular time, you can use an amortization table or an online mortgage calculator. These tools show how much of each monthly payment goes toward the principal and interest.
For example, after 5 years, there will be 5 * 12 = 60 payments made. By using an amortization table or mortgage calculator, you can find the remaining balance after those 60 payments. To calculate the equity, subtract the remaining balance from the original loan amount:
Equity = $280,000 - Remaining balance after 5 years.
Repeat the same process for 10 years and 20 years to find the equity after those periods. Keep in mind that this calculation disregards any appreciation value of the house.