How to Calculate Payments on a Personal Loan

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A personal loan is a lending agreement in which an individual borrows money from another party, agreeing to make interest payments and return the principal. The payments are calculated so that the sum of their present values is equal to the present value of the loan, which is the principal. The main variables are the interest rate, the number of payment periods, and the duration of the loan. There are many online loan payment calculators, but you also can use a simple present value formula for calculating the payment amount.

Formula for Calculating Loan Payments

  • The formula for calculating loan payments is based on the time value of money, which in turn is based on the notion that a dollar today is more valuable than a dollar received any time in the future, because a dollar today can be invested in a risk-free security and earn a return. The formula for calculating loan payments is: r/(1-(1+r)^-n)), where r is the stated interest rate, and n is the number of payments made. Both "r" and "n" will not be annual amounts if payment is made more than once per year. For example, if the stated interest rate is 6 percent and payments are made monthly, r equals 6 percent divided by n, which is 12 months, resulting in an r of 0.5 percent.

Sample Calculation

  • If a $100 loan is made at an annual percentage rate of 6 percent, which is paid monthly, monthly payment is calculated as the monthly rate, 0.5 percent, divided by: (1 minus (1+.01)^-12), or 0.058095. For clarity, the second part of this equation is raised to the power of negative 12. Therefore, .5 percent divided by 0.058095 equals 0.086066. This figure is multiplied by the loan amount, $100, resulting in a monthly payment of $8.61.

References

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