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Ten years ago your firm borrowed $3 million to purchase an office building using a loan with a 7.8% APR and monthly payments for 30 years. How much do you owe on the loan now?

User Jony
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1 Answer

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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.

User Rajkumar
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