# Amortized Loan Calculator

When purchasing a new home, most buyers choose to finance a portion of the purchase price via the use of a mortgage. Amortized Loan (also known as mortgage) calculators are used to determine monthly repayments. The major variables in a mortgage calculation include outstanding loan, tenure of loan years, number of compounding per year, interest rate, monthly (total) repayment. • Mortgage Amount (Outstanding loan) – The original principal on a new loan or principal remaining on an existing loan.
• Tenure of loan years – number of years for the mortgage loan.
• Number of compounding per year – The number of payments required to repay the loan.
• Interest Rate – The annual nominal interest rate, or stated rate of the loan.
• Total (Monthly) Payment – The amount to be paid toward the loan at each monthly payment due date which includes the principal repayment plus the interest paid in each month.

## Amortized Loan Formula

• `Principal repayment = P * (r / n) * (1 + r/n)t*n / [(1 + r/n)t*n - 1] - P * (r/n)`
• `Interest paid = P * (r/n)`
• `Total repayment = P * (r/n) * (1 + r/n)t*n / [(1 + r/n)t*n - 1]`

## Example

Suppose a house mortgage with an outstanding amount of \$6,400,000 of loan that tenure in 20 Years. There are 12 compoundings per year and the interest rate paid is 6.5%. The principal repayment, interest paid and total repayment are \$13,050.01, \$34,666.67, \$47,716.68, respectively.

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