# What is Cumulative Interest?

Cumulative interest is the sum of interest payments made on a loan over its life or over a certain time period. It is calculated by dividing the future value (FV) of the loan by its present value (PV) and then subtracting one. It is typically used to compare the cost of two loans to determine which is more economic. Since interest earned and paid on certain interest-bearing financial instruments, such as bonds and mortgages, are taxable or exempt from U.S. taxes, cumulative interest is also useful when it comes time to complete U.S. tax forms. In contrast to the effective annual percentage rate (APR), annual percentage yield, and discounted cash flow analysis methods, cumulative interest does not take account of the time value of money or initial loan costs, making it a poorer metric of true economic cost.

In the case of a conventional fixed-rate mortgage, interest payments account for a higher percentage of the total monthly payments early in the life of the loan and decrease as a percentage of the total payment as the mortgage ages. Cumulative interest increases at a decreasing rate to a maximum and then declines as a percentage of the total mortgage payment over the life of the loan; this occurs as principal payments make up a larger and larger percentage of the total payment. When calculating cumulative interest, it is assumed that interest compounds periodically with each payment date marking the end of one and the beginning of a new compounding period. In general, market convention is to use annual compounding for consumer loans and mortgages.

Moreover, calculating cumulative interest on adjustable rate mortgages and loans, which charge a variable rate of interest, calls for making some assumptions. The rate of interest on such loans are reset periodically, as should be stated clearly in the terms of the loan. Hence, assumptions of what these future interest rates will be have to be made in order to calculate cumulative interest, or any metric of yield, rate, or cost for that matter. In the calculation of APRs, it is assumed that the initial interest rate will prevail over the life of the loan, for instance. Actual future rates may, and often do, differ from the assumed future rates; they result in significant differences between what the borrower or lender initially calculated the cumulative interest to be and what it in fact turns out to be.

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