Question

Today is Joan's 30th birthday. Assume that she deposits $3,400 today and $3,400 on each of her birthdays until she turns 60 (when she makes the last deposit) into an account earning 6% p.a. She plans to withdraw equal amounts each year from the time she turns 65 until she is 80. The maximum amount that each withdrawal can be is $______.

Answer #1

FV at age 61

FV_{Annuity Due} = c*(((1+ i)^n - 1)/i)*(1 + i ) |

C = Cash flow per period |

i = interest rate |

n = number of payments |

FV= 3400*(((1+ 6/100)^31-1)/(6/100))*(1+6/100) |

FV = 305625.25 |

FV at age 65

Future value = present value*(1+ rate)^time |

Future value = 305625.25*(1+0.06)^(65-61) |

Future value = 385844.84 |

Withdrawals

PV_{Annuity Due} = c*((1-(1+ i)^(-n))/i)*(1 + i ) |

C = Cash flow per period |

i = interest rate |

n = number of payments |

385844.84= Cash Flow*((1-(1+ 6/100)^-16)/(6/100))*(1+6/100) |

Cash Flow = 36019.03 |

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