Question

**1.) **Suppose a person invests $2000
per year (at the end of each year) in a retirement account. The
value of the account depends on the invest rate being paid and the
number of years for which contributions are made. To investigate
this, calculate the future value of such an account after 15,20,25
and 30 years using an annual interest rate of 4%, 6%, 8% and 12%.
organize the results in a table and show your calculations.

**2.) a)** Describe the effects on the future value
of changing the following (cite examples)

i) the number of years while keeping everything else fixed,

ii) the interest rate while keeping everything else fixed,

**b)** Which has a bigger effect on the
future value, doubling the the time from 15 to 30 years or doubling
the interest rate from 4% to 8%? (cite examples)

**3)** In this question assume the interest rate
stays at 6%

**a)** What effect would doubling the
contribution(to $4000 per year) have on the future value of the
account (if everything else is kept fixed) ?

**b)**Is the effect larger or smaller
than the effect of doubling the time from 15 years to 30 years(
while keeping everything else fixed)

**4) **Based on your answers 1-3, which
variable has the largest effect on the future value of a retirement
account: time over which contributions are made, interest rate, or
contribution amount?

Answer #1

future value |
||||

year/rate |
4% | 6% | 8% | 12% |

15 | 40,047.18 | 46,551.94 | 54,304.23 | 74,559.43 |

20 | 59,556.16 | 73,571.18 | 91,523.93 | 144,104.88 |

25 | 83,291.82 | 109,729.02 | 146,211.88 | 266,667.74 |

30 | 112,169.88 | 158,116.37 | 226,566.42 | 482,665.37 |

we can clearly conclude that that as the interest rate increased the future value is increased

similarly as the no of year of investment is increased the future value is also increased.

year/rate |
0.04 | 0.06 | 0.08 | 0.12 |

15 | =-FV(4%,15,2000,0) | =-FV(6%,15,2000,0) | =-FV(8%,15,2000,0) | =-FV(12%,15,2000,0) |

20 | =-FV(4%,20,2000,0) | =-FV(6%,20,2000,0) | =-FV(8%,20,2000,0) | =-FV(12%,20,2000,0) |

25 | =-FV(4%,25,2000,0) | =-FV(6%,25,2000,0) | =-FV(8%,25,2000,0) | =-FV(12%,25,2000,0) |

30 | =-FV(4%,30,2000,0) | =-FV(6%,30,2000,0) | =-FV(8%,30,2000,0) | =-FV(12%,30,2000,0) |

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