The remaining balance on the loan after 10 years is $2,227,876.59
The Breakdown
Loan amount (Principal): $3,000,000
Annual Percentage Rate (APR): 7.8%
Loan term: 30 years (360 months)
Calculating the monthly interest rate by dividing the APR by 12 (number of months in a year):
Monthly interest rate = 7.8% / 12 = 0.65%
Using the loan balance formula to calculate the remaining balance on the loan:
Remaining balance = P × (1 + r)^n - (PMT × ((1 + r)^n - 1) / r)
Where:
P = Loan amount (Principal)
r = Monthly interest rate
n = Total number of payments (loan term in months)
PMT = Monthly payment
To calculate the monthly payment (PMT), we can use the loan payment formula:
PMT = P × (r × (1 + r)^n) / ((1 + r)^n - 1)
Let's calculate the monthly payment (PMT) first:
PMT = 3,000,000 × (0.0065 × (1 + 0.0065)³⁶⁰) / ((1 + 0.0065)³⁶⁰ - ¹)
PMT ≈ $20,964.62
Calculating the remaining balance after 10 years (120 months):
Remaining balance = 3,000,000 × (1 + 0.0065)¹²⁰ - (20,964.62 × ((1 + 0.0065)¹²⁰ - ¹) / 0.0065)
Remaining balance ≈ $2,227,876.59
Therefore, the remaining balance on the loan after 10 years is $2,227,876.59.