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.
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
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