The Time Value of Money

Argosy University

FIN 401 A01

24 September 2014

The Time Value of Money

Issue A:

For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time?

To get the solution to this problem one can keep track yearly as indicated in the below chart. Another way as the book states to calculate the future value for a single amount is to use the formula FV=PV(1+i)n. In this formula with the amounts in this problem FV = Future value, PV =Present value ($500), I = Interest rate (5%) and N =Number of periods (19 years). The total for this is $16,032.977 or in cash value $16,032.98.

If Mary closes the account right after the 20th payment of $500 she would receive $16,532.98. Providing she would might be able to leave this amount in long enough for the interest to pay she would receive $17,359.63. This 5% yearly interest would give her an extra $1326.65 from that last $500 payment. This would be a good investment for the time this payment would be in the account.

YEAR (n) | Yearly deposit (PV) |   | previous year balance (FV) |   | 5% per year (i) |   | End year balance (FV) |

1 | 500 | + |   | * | 1.05 | = | $525.00 |

2 | 500 | + | 525.00 | * | 1.05 | = | $1,076.25 |

3 | 500 | + | 1,076.25 | * | 1.05 | = | $1,655.06 |

4 | 500 | + | 1,655.06 | * | 1.05 | = | $2,262.81 |

5 | 500 | + | 2,262.81 | * | 1.05 | = | $2,900.95 |

6 | 500 | + | 2,900.95 | * | 1.05 | = | $3,571.00 |

7 | 500 | + | 3,571.00 | * | 1.05 | = | $4,274.55 |

8 | 500 | + | 4,274.55 | * | 1.05 | = | $5,013.28 |

9 | 500 | + | 5,013.28 | * | 1.05 | = | $5,788.94 |

10 | 500 | + | 5,788.94 | * | 1.05 | = | $6,603.39 |

11 | 500 | + | 6,603.39 | * | 1.05 | = | $7,458.56 |

12 | 500 | + | 7,458.56 | * |...