Question: The price of a home is $180,000. The bank requires a 10% down payment. After the down payment, the balance is financed with a 30 year fixed mortgage at 6.3%. Determine the unpaid balance after ten years.
Answer: The unpaid balance after ten years is $136,641.85
I have the answer but I need help figuring out the formula used and the steps taken to get the answer. Please help.
First you have to find the payment.
You did not say, but I will assume that the payments are monthly.
let the payment be p
162000 = p( 1 - 1.00525^-360)/.00525
p = 1002.74
unpaid balance after 10 years
= balance if you had paid nothing - amount of the annuity for 10 years
= 162000(1.00525)^120 - 1002.74(1.00525^120 - 1)/.00525
= 136641.30
could be round-off error on their part, I kept max number of decimals using calculator's memories.
To calculate the unpaid balance after ten years, we need to determine the amount that remains to be paid on the mortgage at that point. Let's break down the steps to calculate it:
Step 1: Calculate the down payment
Since the bank requires a 10% down payment, we can find its value by multiplying the price of the home by 10%:
Down Payment = $180,000 x 10% = $18,000
Step 2: Calculate the principal loan amount
The principal loan amount is the initial balance of the mortgage, which is equal to the total price of the home minus the down payment:
Principal Loan Amount = $180,000 - $18,000 = $162,000
Step 3: Calculate the monthly mortgage payment
To calculate the monthly mortgage payment, we need to use the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = monthly mortgage payment
P = principal loan amount
i = monthly interest rate (annual interest rate / 12)
n = total number of monthly payments (30 years x 12 months)
In this case, the annual interest rate is 6.3% and the loan term is 30 years.
First, we need to calculate the monthly interest rate:
Monthly Interest Rate = 6.3% / 100 / 12 = 0.00525
Next, we need to calculate the total number of payments:
Total Number of Payments = 30 years x 12 months = 360 months
Now, we can use the formula to calculate the monthly mortgage payment:
Monthly Mortgage Payment = $162,000 [ 0.00525(1 + 0.00525)^360 ] / [ (1 + 0.00525)^360 - 1 ]
Using a financial calculator or spreadsheet software, this calculation results in a monthly mortgage payment of $1,007.04.
Step 4: Calculate the unpaid balance after ten years
To find the unpaid balance after ten years, we need to calculate how much of the principal loan amount has been paid off in ten years.
First, we need to calculate the total number of payments made in ten years, which is equal to ten years multiplied by twelve payments per year:
Total Number of Payments Made = 10 years x 12 months = 120 months
Next, we determine the remaining balance after ten years by subtracting the total payments made from the principal loan amount:
Unpaid Balance After Ten Years = $162,000 - ($1,007.04 x 120)
Using a calculator, the unpaid balance after ten years is calculated to be $136,641.85.
So, the unpaid balance after ten years is $136,641.85.