How to Calculate the Length of a Loan
The length of a loan is the time it takes to pay it off. Typically, your monthly payment is fixed, but it includes changing interest and principal portions. With any fixed amount above the interest due on the original balance, the loan balance continually decreases until it's paid off. Once you know the loan amount, monthly payment and interest rate, you can calculate the loan's length. Financial calculators make this easy to do once you know how to use them..
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Loan Basics
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Loans amortize, or diminish, in the following process. The monthly interest rate determines how much interest you owe for the month on the loan's original amount. The fixed amount of your payment above the interest pays down the loan balance. Your next month's interest is now less because of the lower balance. Your principal pay-back is now more because of the lower amount of interest. This goes on until the loan is paid off. The interest amount keeps getting smaller and the principal amount keeps getting larger.
Methods
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You can manually calculate each month's interest and principal portions and declining loan balance. When the loan balance hits 0, you can count up the months it takes to get there. You can also use a formula to calculate the loan length. You can also use a financial calculator. The loan length is commonly called N (or NP) for number of periods (or payments). You're calculating N months. To convert into years, divide by 12.
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Formula
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The formula for calculating N is this: (log(1/(1-(LR/P)))/log(1+R)) -- Multiply the loan amount (L) by the periodic interest rate (R), divide by the payment amount (P), subtract from 1 and divide 1 by that number. The result is the compounded interest rate for the whole length. Find the exponent that converts 1 + the periodic rate into the compounded rate. Calculators use log to the base 10, so you have to convert bases. Log compounded rate divided by log periodic rate equals N. (You can also -log (1-(LR/P) for the numerator.)
Financial Calculator
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For quick results, use a financial calculator. You may need to set payment due to end of period. The loan amount is the present value (pv) of your future payments. Enter the present value, the payment amount and the periodic interest rate. N is calculated for you. You may be asked to enter the periodic rate as a percentage. With financial calculators, you have to be careful about entering dollar amounts as either positive or negative numbers. When calculating for N, do not enter the loan and payment amount both positive or both negative. You must enter one positive and one negative.
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References
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