Your Company Took Out A Commercial Mortgage For $8,000,000 To Buy An Office Building. The Mortgage Has An Interest Rate Of 3% (APR) And Is Amortized Over 30 Years, Using Fixed Monthly Payments. However, The Mortgage Must Be Paid Off After 19 Years With A Balloon Payment
To calculate the fixed monthly payments, we first need to find the monthly interest rate.
The annual interest rate (APR) is 3%, so the monthly interest rate will be 3% divided by 12 months, which is 0.25% (0.03/12 = 0.0025).
Now, using the formula for the monthly payment on an amortizing loan:
Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal loan amount ($8,000,000)
r = Monthly interest rate (0.0025)
n = Total number of payments (30 years * 12 months = 360 monthly payments)
Payment = 8,000,000 * 0.0025 * (1 + 0.0025)^360 / ((1 + 0.0025)^360 - 1)
Using a calculator, the fixed monthly payment comes out to be $38,146.03.
Now, since the mortgage must be paid off after 19 years, we need to calculate the remaining principal balance at the end of the 19th year.
The total number of payments made in 19 years would be 19 * 12 = 228 payments.
To find the remaining principal balance, we can calculate the outstanding loan amount using the formula for the remaining balance on an amortizing loan:
Remaining balance = P * ((1 + r)^n - (1 + r)^p) / ((1 + r)^n - 1)
Where:
P = Principal loan amount ($8,000,000)
r = Monthly interest rate (0.0025)
n = Total number of payments (30 years * 12 months = 360 monthly payments)
p = Number of payments made (19 years * 12 months = 228 payments)
Remaining balance = 8,000,000 * ((1 + 0.0025)^360 - (1 + 0.0025)^228) / ((1 + 0.0025)^360 - 1)
Using a calculator, the remaining balance comes out to be $3,729,209.82.
Finally, the balloon payment required to pay off the remaining balance after 19 years would be $3,729,209.82.
To calculate the fixed monthly payment for the commercial mortgage, we can use the formula for amortized loans:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
PV = Present value (loan amount)
r = Monthly interest rate
n = Total number of payments
First, let's calculate the monthly interest rate:
r = (3% / 100) / 12
r = 0.0025
Next, let's calculate the total number of payments:
n = 30 years * 12 months/year
n = 360
Now, let's calculate the present value (loan amount):
PV = $8,000,000
Putting the values into the formula:
P = (0.0025 * 8,000,000) / (1 - (1 + 0.0025)^(-360))
Using a calculator or spreadsheet software, the monthly fixed payment comes out to be approximately $38,321.03.
Now that we know the monthly payment, let's calculate the balloon payment after 19 years:
First, calculate the total number of payments made by that point:
Total payments made = 19 years * 12 months/year
Total payments made = 228
Next, calculate the remaining loan balance at that point:
Remaining balance = PV * (1 + r)^Total payments made - (P * ((1 + r)^Total payments made - 1) / r)
Remaining balance = 8,000,000 * (1 + 0.0025)^228 - (38,321.03 * ((1 + 0.0025)^228 - 1) / 0.0025)
Using a calculator or spreadsheet software, the balloon payment comes out to be approximately $6,437,501.06.
Therefore, after 19 years, you will need to make a balloon payment of around $6,437,501.06 to pay off the mortgage.