What is interest?
Interest is both the cost of borrowing funds and the profit that accrues to those who deposit funds in a savings account. Calculated as a percentage of the loan or deposit balance, interest is paid to the lender by the borrower in the case of a loan or from the financial institution to the depositor in the case of a savings account.
Interest refers to two related but very distinct concepts: either the amount a borrower pays the bank for the cost of lending or the amount an account holder receives for the favor of leaving money with the bank.
There are two basic kinds of interest: simple interest and compound interest. Simple interest, or flat-rate interest, is calculated as a percentage of a deposit or loan’s principal balance. No matter how long a borrower goes without paying a debt or an account holder keeps money in the bank, interest will still be calculated from the original amount.
With compound interest, accrued interest is added to the principle balance. Think of it as interest on interest. The formula to calculate compound interest is: A = P (1 + r/n) (nt), where A is the future value of the loan or investment, including interest; P is the principal investment amount; r is the annual interest rate (decimal); n is the number of times that interest is compounded each year; and t is length of the loan. Allegedly, Albert Einstein humorously referred to compound interest as the the most powerful force in the universe.
All loans incur interest. With auto loans, mortgages, and student loans, interest payments are rolled into the monthly payment. When the terms of the loan are negotiated, the parties can agree to a specific life span for the debt instrument: a five-year auto loan or a 15-year mortgage, for instance. The exception is revolving loans such as credit cards that only accrue interest on unpaid balances. Interest on loans is often expressed as an annual percentage rate, or APR, which takes into account other administrative fees.
However, not all depository accounts accrue interest. With few exceptions, checking accounts, for example, never accrue interest, and basic savings accounts accrue interest at such low rates that many investors have chosen to put their money in more profitable instruments.
Simple interest: you borrow $1,000 and the annual interest rate is 15 percent, then you must pay $150 in interest after a year ($1,000 x 0.15 = $150). Accrued simple interest is calculated based on the original amount of the loan without any extra fees or other interest.
Compound interest: you have $5,000 in your savings account with an annual interest rate of five percent. Compounded monthly, the value of this investment after 10 years can be computed as follows: P = 5,000, r = 0.05, n = 12, t = 10. Plug these figures into the formula and you get: A = 5,000 (1 + 0.05 / 12) ^ (12(10)). The balance in the account after 10 years would be $8,235.05.