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Compound interest is the interest you earn on the interest you've earned, as well as on the original amount invested. This is a little more realistic, as most people just leave their money in their account and let the interest grow. Because you're getting interest on the interest as well as the principal. compound interest grows faster. Let's look at an example of compound interest, but work it out using the simple interest formula so you can see how the money is growing. Example 1: You deposit $2000 in an account that pays 1.5% per annum, compounded semi-annually, and leave it for 2 years. Find the total interest earned, and the total amount you end up with. We're introducing several new terms here. 'Per annum' means 'per year'. 'Compounded semi-annually' is telling you that interest is paid twice a year (every 6 months), and you leave the interest in your account. After the first 6 month period: I = r·t·P I = 6/12 x 0.015 x 2000 I = $15 You leave this in the account, so the total amount A = 2000 + 15 = $2015 This becomes the principal for the second six-month period. After the second 6 month period: I = r·t·P I = 6/12 x 0.015 x 2015 I = $15.11 You leave this in the account, so the total amount A = 2015 + 15.11 = $2030.11 This becomes the principal for the third six-month period. After the third 6 month period: I = r·t·P I = 6/12 x 0.015 x 2030.11 I = $15.23 You leave this in the account, so the total amount A = 2030.11 + 15.23 = $2045.34 This becomes the principal for the third six-month period. After the fourth 6 month period: I = r·t·P I = 6/12 x 0.015 x 2045.34 I = $15.34 You leave this in the account, so the total amount A = 2045.34 + 15.34 = $2060.68 The total amount in your acount is $2060.68 The total interest earned was $2060.68 - $2000 = $60.68 Comparison: If you'd taken out the interest every six months, the simple interest would have been: I = t·r·P I = 2 x 0.015 x 2000 I = $30 Leaving the interest in earned you an extra $30.68 This method worked OK, but we will need a faster way to do the calculation, because many financial institutions calculate your interest daily. In the above example, that would require 2 x 365 = 730 steps! Let's look at the Compound Interest Formula ... |