Compound Interest



Compound Interest

|P |Frequency of compounding |n |r |t |A |

| |per year | | | | |

|$ 1.00 |annual |1 |1 |1 |$ 2.00 |

|$ 1.00 |semi-annual |2 |1 |1 |$ 2.25 |

|$ 1.00 |quarterly |4 |1 |1 |$ 2.44140625 |

|$ 1.00 |monthly |12 |1 |1 |$ 2.61303529022468 |

|$ 1.00 |weekly |52 |1 |1 |$ 2.69259695443717 |

|$ 1.00 |daily |365 |1 |1 |$ 2.71456748202201 |

|$ 1.00 |hourly |8760 |1 |1 |$ 2.71812669161742 |

|$ 1.00 |by the second |31536000 |1 |1 |$ 2.71828178130246 |

|$ 1.00 |continuously |continuously |1 |1 |$ 2.71828182845905 |

We start by using the interest formula [pic]. Where the variables are defined as:

[pic] is the total amount of money in the account

[pic] is the principal, the starting amount.

[pic] is the interest rate, which must be expressed in decimal form.

[pic] is the number of time compounded per year.

[pic] is time in years.

Notice that the last line is continuously compounded interest, using the formula[pic], and the value of [pic] is equal to value of [pic].

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