Question

1. John wishes to make a quarterly deposit into his savings account so that at the end of 10 years the account balance will be $10,000. If the account earns 6% annual interest, compounded quarterly, how much should he deposit each quarter?

2. The maintenance on a machine is expected to be $155 at the end of the first year, then increasing by $35 each year for the next 7 years. What sum of money would need to be set aside now to pay the maintenance for the 8-year period? Assume 6% interest.

Please help answer both questions.

Answer #1

**(1)**

Quarterly interest rate = 6% / 4 = 1.5%

Number of quarters = 4 x 10 = 40

Quarterly deposit ($) = 10,000 / F/A(1.5%, 40) = 10,000 /
54.2679** = **184.27**

**F/A(r%, N) = [(1 + r)^{N} - 1] / r

F/A(1.5%, 40) = [(1.015)^{40} - 1] / 0.015 = (1.8140 -
1) / 0.015 = 0.8140 / 0.015 = 54.2679

(2)

Money to be set aside now is equal to the Present Worth (PW) of the costs, computed as follows.

PV factor for year N = (1.06)^{-N}

Year | Cost ($) | PV Factor @6% | Discounted Cost ($) |

(A) | (B) | (A) x (B) | |

1 | 155 | 0.9434 | 146.23 |

2 | 190 | 0.8900 | 169.10 |

3 | 225 | 0.8396 | 188.91 |

4 | 260 | 0.7921 | 205.94 |

5 | 295 | 0.7473 | 220.44 |

6 | 330 | 0.7050 | 232.64 |

7 | 365 | 0.6651 | 242.75 |

8 | 400 | 0.6274 | 250.96 |

PW of Costs ($) = | 1,656.97 |

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Rup is planning to retire in 35 years. He wishes to
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