Compound Interest Formula source.docx

The number of years the money is invested or borrowed

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= the number of years the money is invested or borrowed for Note that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. Should you wish to calculate the compound interest only, you need this: Total compounded interest = P (1 + r/n) (nt) - P Let's look at an example Compound interest formula (including principal): A = P(1+r/n) ( n t ) If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly , the value of the investment after 10 years can be calculated as follows... P = 5000. r = 5/100 = 0.05 (decimal). n = 12. t = 10. If we plug those figures into the formula, we get: A = 5000 (1 + 0.05 / 12) ^ (12(10)) = 8235.05. So, the investment balance after 10 years is $8,235.05. Methodology A few people have written to me asking me to explain step-by-step how we get the 8235.05. This all revolves around PEMDAS (also known as BODMAS in the UK ) and the order of operations. Let's go through it: A = 5000 (1 + 0.05 / 12) ^ (12(10)) (note that ^ means 'to the power of') Using the order of operations we work out the totals in the brackets first. Within the first set of brackets, you need to do the division first and then the addition (division and multiplication should be carried out before addition and subtraction). We can also work out the 12(10). This gives us... A = 5000 (1 + 0.00416) ^ 120 (note that the over-line in the calculation signifies a decimal that repeats to infinity. So, 0.00416666666...)
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Then: A = 5000 (1.00416) ^ 120 The exponent goes next. So, we calculate (1.00416) ^ 120.
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