# VALENCIA MTB 1103 - Compound interest

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Compound interest is the interest paid on the original principal and on the accumulated past interest When you borrow money from a bank you pay interest Interest is really a fee charged for borrowing the money it is a percentage charged on the principal amount for a period of a year usually If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage you will need to understand how compound interest works Compound Interest Example Think of it like this If you start out with 100 dollars and you receive 10 dollars as interest at the end of the first period you would have 110 dollars that you can earn interest on in the second period So in the second period you would earn 11 dollars interest Now for the 3rd period you have 110 11 121 dollars that you can earn interest on So at the end of the 3rd period you will have earned interest on the 121 dollars The amount would be 12 10 So you now have 121 12 10 132 10 of which you can earn interest The following formula calculates this in one step rather then doing the calculation for each compounding period one step at a time Compound Interest Formula Compound interest is calculated based on the principal interest rate APR or annual percentage rate and the time involved P is the principal the initial amount you borrow or deposit r is the annual rate of interest percentage n is the number of years the amount is deposited or borrowed for A is the amount of money accumulated after n years including interest When the interest is compounded once a year A P 1 r n A P 1 r 5 However if you borrow for 5 years the formula will look like This formula applies to both money invested and money borrowed Frequent Compounding of Interest What if interest is paid more frequently It s not much more complicated except the rate changes Here are a few examples of the formula Annually P 1 r annual compounding Quarterly P 1 r 4 4 quarterly compounding Monthly P 1 r 12 12 monthly compounding Compound Interest Table Confused It may help to examine a graph of how compound interest works Say you start with 1000 and a 10 interest rate If you were paying simple interest you d pay 1000 10 which is another 100 for a total of 1100 if you paid at the end of the first year At the end of 5 years the total with simple interest would be 1500 The amount you pay with compound interest depends on how quickly you pay off the loan It s only 1100 at the end of the first year but is up to over 1600 at 5 years If you extend the time of the loan the amount can grow quickly Year Initial Loan InterestLoan at End 0 1 2 3 4 5 1000 00 1100 00 1210 00 1331 00 1464 10 1610 51 1 000 00 10 100 00 1 100 00 1 100 00 10 110 00 1 210 00 1 210 00 10 121 00 1 331 00 1 331 00 10 133 10 1 464 10 1 464 10 10 146 41 1 610 51

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