The Turners have purchased a house for $160,000. They made an initial down payment of $40,000 and secured a mortgage with interest charged at the rate of 9%/year compounded monthly on the unpaid balance. The loan is to be amortized over 30 yr. (Round your answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$
(b) How much total interest will they pay on the loan?
$
(c) What will be their equity after 10 years?
$
(d) What will be their equity after 22 years?
$
(a) Well, well, well, the Turners are in quite a pickle! To find out their monthly payment, we need to break out the ol' calculator and do some math. Let's see...
First, we need to calculate the unpaid balance on the loan. They bought the house for $160,000, made a down payment of $40,000, so the remaining balance on the loan is $160,000 - $40,000 = $120,000.
Next, we need to find the monthly interest rate. The annual interest rate is 9%, so the monthly interest rate would be 9% / 12 = 0.75%.
Now, to calculate the monthly payment, we'll use the formula for a loan payment:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value (unpaid balance)
n = number of payments (in this case, 30 years * 12 months = 360)
Plug in the values and let's calculate! *drumroll please*
P = (0.0075 * 120,000) / (1 - (1 + 0.0075)^(-360))
After doing the math, the monthly payment comes out to be approximately $952.25.
(b) Ahh, interest, the bane of every borrower's existence. To calculate the total interest paid, we'll use the formula:
Total Interest = (P * n) - PV
Plug in the values and let's find out how much the Turners will be pouring down the drain!
Total Interest = (952.25 * 360) - 120,000
After some number crunching, the total interest paid on the loan would be approximately $173,410.80. Yikes!
(c) After 10 years, the Turners must be eager to see how much equity they've built up. To find out, we need to calculate the remaining balance on the loan after 10 years. We'll use the formula:
Remaining Balance = PV * (1 + r)^n - P * (((1 + r)^n - 1) / r)
Where:
PV = present value (unpaid balance)
r = monthly interest rate
n = number of payments (10 years * 12 months = 120)
Plug in the numbers, crunch them down, and voila!
Remaining Balance = 120,000 * (1 + 0.0075)^120 - 952.25 * (((1 + 0.0075)^120 - 1) / 0.0075)
After all the calculations, the equity after 10 years would be approximately $106,921.23.
(d) Now, let's fast forward to 22 years later. How much equity will the Turners have built up by then? We'll use the same formula as before, but this time the number of payments would be 22 years * 12 months = 264.
Remaining Balance = 120,000 * (1 + 0.0075)^264 - 952.25 * (((1 + 0.0075)^264 - 1) / 0.0075)
After some number crunching, their equity after 22 years would be approximately $58,733.45.
So, there you have it! The monthly payment is approximately $952.25, the total interest paid is approximately $173,410.80, the equity after 10 years is approximately $106,921.23, and the equity after 22 years is approximately $58,733.45. Good luck to the Turners in their homeownership journey!
To find the answers to these questions, we can use the formula for calculating the monthly payment of a mortgage:
Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal (initial loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments (number of years multiplied by 12)
Let's calculate the answers step by step:
(a) Monthly Payment:
The principal (P) is the loan amount minus the down payment: $160,000 - $40,000 = $120,000.
The monthly interest rate (r) is the annual interest rate divided by 12: 9% / 12 = 0.0075.
The total number of monthly payments (n) is the number of years multiplied by 12: 30 * 12 = 360.
Using the formula, we can calculate the monthly payment:
Monthly Payment = $120,000 * (0.0075 * (1 + 0.0075)^360) / ((1 + 0.0075)^360 - 1)
Monthly Payment ≈ $964.53
Therefore, the Turners will be required to make a monthly payment of approximately $964.53.
(b) Total Interest Paid:
To calculate the total interest paid on the loan, we can multiply the monthly payment by the total number of payments (n) and subtract the principal (P):
Total Interest Paid = (Monthly Payment * n) - P
Total Interest Paid = ($964.53 * 360) - $120,000
Total Interest Paid ≈ $247,032.80
Therefore, the Turners will pay approximately $247,032.80 in total interest over the life of the loan.
(c) Equity after 10 years:
To calculate their equity after 10 years, we need to determine the remaining balance on the loan. To do this, we need to calculate the number of payments made in 10 years and subtract it from the total number of payments (n):
Number of payments made in 10 years = 10 * 12 = 120
Remaining balance = P * ((1 + r)^n - (1 + r)^m) / ((1 + r)^n - 1)
Remaining balance = $120,000 * ((1 + 0.0075)^360 - (1 + 0.0075)^120) / ((1 + 0.0075)^360 - 1)
Remaining balance ≈ $102,616.51
Equity after 10 years = House value - Remaining balance
Equity after 10 years = $160,000 - $102,616.51
Equity after 10 years ≈ $57,383.49
Therefore, the Turners will have approximately $57,383.49 in equity after 10 years.
(d) Equity after 22 years:
To calculate their equity after 22 years, we follow the same process:
Number of payments made in 22 years = 22 * 12 = 264
Remaining balance = P * ((1 + r)^n - (1 + r)^m) / ((1 + r)^n - 1)
Remaining balance = $120,000 * ((1 + 0.0075)^360 - (1 + 0.0075)^264) / ((1 + 0.0075)^360 - 1)
Remaining balance ≈ $17,372.64
Equity after 22 years = House value - Remaining balance
Equity after 22 years = $160,000 - $17,372.64
Equity after 22 years ≈ $142,627.36
Therefore, the Turners will have approximately $142,627.36 in equity after 22 years.