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?
I = PRT
I = 300,000 * 0.07 * 30
I = 630,000
630,000 + 630,000 = 930,000
23,500 * 30 = 705,000
930,000 - 705,000 = _______ balloon payment
Why is 630,000 added twice? and that doesn't = 930,000
Teacher said answer would be about 3 times the annual payment, like having to make 3 payments at the end.
Can someone please help?
My goof.
This line 630,000 + 630,000 = 930,000
should be 630,000 + 300,000 = 930,000
Be sure to subtract as I showed in the last step.
To calculate the balloon payment at the end of the 30-year mortgage term, we need to first determine the remaining balance on the loan after making the annual payments.
The annual payment of $23,500 represents the amount paid towards the principal and interest over one year.
To find the remaining balance after each annual payment, we can use the formula for the present value of an annuity:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value (remaining balance)
PMT = Periodic payment (annual payment)
r = Interest rate per period
n = Number of periods
In this case:
PMT = $23,500
r = 7% per year (0.07)
n = 30 years
Now we can substitute these values into the formula:
PV = 23500 × [(1 - (1 + 0.07)^(-30)) / 0.07]
Calculating this expression, we find that the remaining balance on the mortgage loan after 30 years of annual payments is approximately $81,685.82.
Therefore, the balloon payment at the end of the mortgage term would be equal to the remaining balance, which is approximately $81,685.82.