Early Loan Repayment

Early Loan Repayment

If the Center takes out a 5-year term loan that would be repaid in equal annual installments, how much will it owe to BankSouth if Gary decides to pay off the loan early, at the end of the third year? (Use the term loan interest rate offered by the bank you selected for a term loan in question 1.)

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Early Loan Repayment

Early Loan Repayment refers to the act of paying off a loan before the agreed-upon end of its term. Borrowers may choose to repay a loan early to reduce the total interest costs, improve financial flexibility, or eliminate debt.

To determine how much will be owed to BankSouth if the Center pays off the loan early at the end of the third year, we need to calculate the outstanding principal after three years, using the loan amortization schedule. Here’s how we can calculate this step-by-step:

1. Determine Loan Details

• Loan Amount (Principal): The amount borrowed (denoted as $P$).
• Loan Term: 5 years.
• Annual Interest Rate: (denoted as $r$).
• Annual Payment: Calculated using the loan formula for equal annual payments.

The formula for the annual payment is:

PMT=P⋅r1−(1+r)−nPMT = \frac{P \cdot r}{1 – (1 + r)^{-n}}PMT=1−(1+r)−nP⋅r​

Where:

• $P$ is the loan amount.
• $r$ is the annual interest rate.
• $n$ is the total number of payments (5 years in this case).

2. Calculate the Remaining Principal

The remaining principal after $t$ years can be calculated using the formula:

Remaining Principal=P⋅(1+r)t−PMT⋅(1+r)t−1r\text{Remaining Principal} = P \cdot (1 + r)^t – PMT \cdot \frac{(1 + r)^t – 1}{r}Remaining Principal=P⋅(1+r)t−PMT⋅r(1+r)t−1​

Where:

• $P$, $r$, and $PMT$ are as defined earlier.
• $t$ is the number of years completed (3 years in this case).

3. Input Details for Calculation

Provide the following information to proceed with the calculation:

• Loan amount ($P$).
• Annual interest rate ($r$).
• Loan term (5 years).