Still don't think this is right.
Mortgage is for $300,000 for 30 years, Fixed interest rate = 7% per year.
Annual payments = $23,500
At end of 30 years, must make balloon payment. How much is the balloon payment?
My teacher said it will be like making 3 payments at the end.
I am not familiar with a "balloon payment" since I am not from the US, but I will take a stab at the math.
Amount owing after 30 years
= 300000(1.07)^30 - 23500( 1.07^30 - 1)/.07
= $ 63,848.80
Is this the balloon payment?
It is appr 3 times the annual payment of 23,500
The actual annual payment needed to pay off the $300,000 in 30 years would have been
300000(.07)/( 1 - 1.07^-30)
= $24,175.92 , our payment of $23,000 was not enough so clearly there would have been a balance at the end of the year.
Confirm if this is what is meant by the "balloon payment"
To calculate the balloon payment at the end of 30 years, we need to understand the structure of the mortgage and the payments made over the years.
In this case, you have a mortgage of $300,000 for 30 years with a fixed interest rate of 7% per year. The annual payments are $23,500.
First, we need to determine the remaining loan balance at the end of the 30 years. To do this, we need to calculate the loan balance after each annual payment.
The loan balance after each payment is calculated by deducting the principal portion of the payment from the outstanding loan balance and adding the interest accrued over the year.
The principal portion of the payment is calculated by subtracting the interest accrued over the year from the total annual payment.
To calculate the interest accrued for each year, we multiply the outstanding loan balance at the beginning of the year by the interest rate.
The outstanding loan balance after 30 years will be the balloon payment.
Now let's calculate the balloon payment step by step:
1. Calculate the interest accrued for the first year:
Interest Accrued = Outstanding Loan Balance * Interest Rate
Interest Accrued = $300,000 * 7% = $21,000
2. Calculate the principal portion of the payment for the first year:
Principal Portion = Total Annual Payment - Interest Accrued
Principal Portion = $23,500 - $21,000 = $2,500
3. Calculate the outstanding loan balance after the first year:
Remaining Balance = Outstanding Loan Balance - Principal Portion
Remaining Balance = $300,000 - $2,500 = $297,500
4. Repeat steps 1 to 3 for the next 29 years, adjusting the outstanding loan balance each year.
5. After the 30th year, the balloon payment will consist of the remaining outstanding loan balance:
Balloon Payment = Remaining Balance after 30 years
By following these steps and performing the calculations, you will determine the balloon payment due at the end of the 30-year mortgage term.