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Author: Admin | 2025-04-27
(1 + r/n)nt – P Where: X = compound interest P = principal amount (original amount) r = annual interest rate (expressed in decimal form) n = the number of compounding periods per unit of time. For example, annually is 1, semi-annually is 2, quarterly is 4, monthly is 12, and weekly is 52. t = the number of time units the principal amount is invested or borrowed for. Differently put, it is the amount of time (expressed in years) through which the money compounds. Example #1 (Interest compounded quarterly) Let us say an investor deposits R10 000 into a savings account at an annual interest rate of 8%, compounded on a quarterly basis, for a period of 5 years. X = P (1 + r/n)nt – P X = 10 000 (1 + 0.08/4)4×5 – 10 000 X = 10 000 (1.02)20 – 10 000 X = 10 000 (1.485947) – 10 000 X = 14 859 – 10 000 X = 4 859 This means the amount in the savings account would grow from R10 000 to R14 859 with the cumulative interest (addition of all interest payments) over the period of 5 years. Example #2 (Interest compounded monthly) When the amount and investment period remain the same as in example 1, but the interest is compounded monthly, the calculation will look as follows: X = P (1 + r/n)nt – P X = 10 000 (1 + 0.08/12)12×5 – 10 000 X = 10 000 (1.006667)60 – 10 000 X = 10 000 (1.489875) – 10 000 X = 14 899 – 10 000 X = 4 899 Example #3 (Interest compounded annually) When the amount and investment period remain the same as in examples 1 and 2, but the interest is compounded annually, the calculation will look as follows: X = P (1 + r/n)nt – P X = 10 000 (1 + 0.08/1)1×5 – 10 000 X = 10 000 (1.08)5 – 10 000 X = 10 000 (1.146932) – 10 000 X = 11 469 – 10 000 X = 1 469 Frequent compounding
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