If want to pay off a loan all at once, in a lump sum, then you just pay off the outstanding balance, if there are no prepayment penalties. If the outstanding balance isn't being updated and there is just a payment schedule, then you'll need to determine the periodic interest rate of the original agreement and then solve for the present value of the future payments to get the amount that's fair for you to pay to pay off the loan. If instead you want to pay a larger periodic payment to pay the loan off earlier but not immediately, then you'd need to calculate the larger payments for the same interest rate but a different number of remaining payments.

- Skill level:
- Moderately Challenging

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### Things you need

- Financial calculator

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## Instructions

- 1
Determine the periodic interest rate of the original agreement using a financial calculator (see Resources). Type in the monthly payment, "P," and press the PMT key. Use just the principal and interest portion for P, not escrow payments. Enter number of payments both past and future and press the "N" key. Enter the original loan amount and press the"PV" (for "present value") key. Press the "i" key and then the "CMPT" key (to compute I).

- 2
Determine the fair value to place on the outstanding payments by calculating the present value for the remaining "N" payments. Enter "N" into your calculator. Then press the "N" key. This will change the value of "N" from the amount you typed in before. Now press "PV" and then "CMPT" to get the current value. This calculation works if the next payment isn't to be made for a month.

- 3
Calculate new, higher payment amounts if you want to pay the loan off sooner, but not immediately, by typing in how many payments you'd like to make to pay it off. Then press the "N" key. Then press "PMT," then "CMPT."

#### Tips and warnings

- Note that the stated, or nominal, interest rate of a loan is the periodic interest rate times the number of payments per year. For example, if the nominal rate is 6% and payments are monthly, then the periodic rate is 6%/12, or 0.005.
- The formula relating P, i, PMT and PV is PV = P * [(1+i)^n - 1]/i, where the asterisk * indicates multiplication and the caret ^ indicates exponentiation. Note that "i" needs a calculator to be solved for quickly.