## Answers

**Answer**

**Computation of Future value and the interest earned for each of the following compounding frequencies:**

**Future value = Present value*(1+i/m)^(n*m)**

where,

n - number of years

m - frequency of compounding in a year

i - rate of interest

**Compound Interest = = P [(1 + i) ^{n} – 1]**

where,

P = Principal,

i = nominal annual interest rate in percentage terms

n = number of compounding periods.

Frequency | P/Y | C/Y | N | I/Y |

Annually | 1 | 1 | 3 | 4% |

Semiannually | 1 | 2 | 3 | 4% |

Quartely | 1 | 4 | 3 | 4% |

Monthly | 1 | 12 | 3 | 4% |

Daily | 1 | 365 | 3 | 4% |

Where,

N – time in years (for compound interest calculations) OR number of payments made during the term of the annuity (for annuity calculations)

I/Y – nominal annual rate of interest per year (entered as a %; NOT a decimal)

C/Y – number of interest compounding periods per year

P/Y – number of payment periods per year

Frequency | PV | PMT | FV | Interest Earned |

Annually | $300.00 | $0.00 | $337.46 | $37.46 |

Semiannually | $300.00 | $0.00 | $337.85 | $37.85 |

Quartely | $300.00 | $0.00 | $338.05 | $38.05 |

Monthly | $300.00 | $0.00 | $338.18 | $38.18 |

Daily | $300.00 | $0.00 | $338.25 | $38.25 |

Where,

PV – present value (the amount of money at the beginning of the transaction.)

PMT – Periodic deposit amount

FV – future value (money at the end of the transaction.)

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