Formula of Amortized Loan

An amortized loan is a loan with a repayment schedule that consists of even payments that cover both principal and interest, so that the loan is paid off at the end of its term. The formula for the periodic payment amount on an amortized loan is:

Periodic Payment Formula (M)

M = L[i(1+i)^n]/[(1+i)^n-1]

Where:

  • M = periodic payment amount
  • L = the loan amount
  • i = periodic interest rate
  • n = total number of payments

Calculating the Periodic Payment Amount (M)

The periodic payment amount for an amortized loan is calculated by multiplying the loan amount by the periodic interest rate, multiplying the result by the sum of all the powers of 1 plus the periodic interest rate, and then dividing that result by the difference between the sum of all the powers of 1 plus the periodic interest rate and 1.

Calculating the Periodic Interest Rate (i)

The periodic interest rate is calculated by dividing the annual interest rate by the number of payments per year. For example, if the annual interest rate is 5% and there are 12 payments per year, then the periodic interest rate would be 0.42% (0.05/12 = 0.0042).

Calculating the Total Number of Payments (n)

The total number of payments is calculated by multiplying the number of years of the loan term by the number of payments per year. For example, if the loan term is 5 years and there are 12 payments per year, then the total number of payments would be 60 (5 x 12 = 60).

Related Questions

  • What is the difference between an amortized loan and a non-amortized loan?
  • What factors go into the calculation of an amortized loan?
  • What is the meaning of the periodic payment amount?
  • How is the periodic interest rate calculated?
  • What is the formula for calculating the total number of payments?
  • What is the purpose of an amortized loan?
  • What are the advantages and disadvantages of an amortized loan?
  • How do I use the amortized loan formula?
  • What other factors should I consider when calculating an amortized loan?
  • What other types of loans can be amortized?