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Let P be the amount of invested money (P = 5,000), and iper cent a year the interest (i = 6).

After one year, the amount becomes P + (i/100)P. This equals P(1 + i/100), so that adding on i per cent is equivalent to multiplying by 1 + i/100.

When interest is compound annually, the new amount is used to calculate the interest due in the second year and so, after two years, the amount becomes P(1 + i/100)^2.

After n years, the amount becomes

P(1 + i/100)^n

which is the formula for compound interest.

So, after 5 years, the amount becomes

P(1 + i/100)^5

= 5,000(1 + 6/100)^5

= 5,000(1 + 0.06)^5

= 5,000(1.06)^5

= 6,691.127888

= 6,691.13

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15y ago

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