An early or delayed loan payoff refers to the process of changing your loan repayment schedule. Early payoff means increasing your monthly payments to pay off the loan faster, while delayed payoff involves extending the loan term, resulting in lower monthly payments but potentially more interest paid over time.

1. Monthly Payment Formula:

\[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]2. Remaining Balance Formula:

\[B = L\frac{(1+r)^p - (1+r)^n}{1 - (1+r)^n}\]Where:

- \(P\) = Monthly payment
- \(L\) = Loan amount
- \(r\) = Monthly interest rate (annual rate divided by 12)
- \(n\) = Total number of months in the loan term
- \(B\) = Remaining balance
- \(p\) = Number of payments made

- Calculate the monthly interest rate: \(r = \frac{\text{Annual Interest Rate}}{12}\)
- Calculate the current monthly payment using the Monthly Payment Formula.
- Calculate the remaining balance using the Remaining Balance Formula.
- Calculate the new monthly payment using the Monthly Payment Formula with the remaining balance and new loan term.
- Calculate the extra monthly payment by subtracting the current payment from the new payment.

Let's calculate the new monthly payment for a $200,000 loan at 4% annual interest, originally for 30 years, with 60 payments made and a new term of 20 years:

- \(r = \frac{4\%}{12} = 0.00333\)
- Current monthly payment: \(P = 200000 \times \frac{0.00333(1+0.00333)^{360}}{(1+0.00333)^{360}-1} = 954.83\)
- Remaining balance: \(B = 200000 \times \frac{(1+0.00333)^{60} - (1+0.00333)^{360}}{1 - (1+0.00333)^{360}} = 183,193.51\)
- New monthly payment: \(P_{new} = 183193.51 \times \frac{0.00333(1+0.00333)^{240}}{(1+0.00333)^{240}-1} = 1,110.20\)
- Extra monthly payment: \(1,110.20 - 954.83 = 155.37\)

The green portion represents the current monthly payment ($954.83), while the red portion shows the extra monthly payment ($155.37) under the new loan terms.

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