Loans And Amortization

A loan is a sum of money borrowed from a lender that must be repaid over time, usually with interest. The borrower agrees to specific terms including the repayment schedule, interest rate, and any fees.

The principal is the original amount of money borrowed, before interest is applied. Each payment you make typically reduces the principal balance while also covering interest charges.

Interest is the cost of borrowing money, expressed as a percentage of the principal. It is the fee the lender charges for providing the loan and is how lenders profit from lending.

Simple interest is calculated only on the original principal throughout the life of the loan. The formula is \[I = P \times r \times t\] where \(P\) is principal, \(r\) is the rate, and \(t\) is time in years.

Compound interest is calculated on both the initial principal and on the accumulated interest from previous periods. This causes interest to grow exponentially over time, dramatically increasing the total cost of borrowing.

A mortgage is a loan specifically used to purchase real estate, where the property itself serves as collateral. If the borrower fails to repay, the lender can foreclose on the property.

A fixed-rate mortgage has the same interest rate for the entire loan term, resulting in identical monthly payments. Common terms are 15, 20, or 30 years, providing predictable payments but often starting with higher rates than ARMs.

An ARM has an interest rate that changes periodically based on a benchmark index plus a margin. Initial rates are typically lower than fixed-rate loans, but payments can increase significantly when rates reset.

An amortization schedule is a table that breaks down each loan payment into principal and interest portions. It shows how the balance decreases over time and the total interest paid over the life of the loan.

Amortization refers to the process of spreading loan payments over time so that the loan is fully repaid by the end of the term. Each payment includes both interest and principal, with the principal portion growing over time.

APR represents the yearly cost of borrowing money, including the interest rate plus certain fees like origination or closing costs. It expresses the true cost of a loan as a standardized annual rate for comparison purposes.

APY is the effective annual rate of return or cost after accounting for the compounding of interest within the year. It is most commonly used for savings accounts but also reflects the true cost of compounding on loans.