Question

Harry is planning to save for retirement over the next 25 years. To do this, he plans to invest $500 per month, and his company will match this with a deposit of $450 per month. The first payment will be made today. He plans to earn an 11% APR (compounded monthly) each year while he save. Assume that Harry will make monthly withdraws beginning the month he retires; also, assume that he plans to earn 3% APR (compounded monthly) on his account balance in retirement, and will have a 20-year withdrawal period. Calculate the amount Harry can withdraw each month in retirement. (Enter a positive value, and round to 2 decimals)

Finnick has just been offered a job earning $75,000 a year. Finnick is paid once per year with his first check received one year from today. He anticipates his salary to grow by 2% per year until his retirement in 40 years. Assuming an interest rate of 10%, calculate the value of his final paycheck (40 years from today). (Enter a positive number and round to 2 decimals)

Answer #1

1) | Total monthly deposit = 500+450 = $950, which is an annuity due | |

as the payments are made at the beginning of each month. | ||

The FV of the annuity (using the formula for finding FV of annuity | ||

due = 950*(1+0.11/12)*((1+0.11/12)^300-1))/(0.11/12) = | $ 15,11,052.13 | |

The amount so accumulated is the PV of the monthly drawals, which is | ||

also an annuity due. | ||

Using the formula for finding the PV of an annuity due, the monthly | ||

amount that can be drawn is equal to: | ||

= 1511052.13*0.0025*1.0025^240/((1.0025*(1.0025^240-1)) = | $ 8,359.36 | |

2) | Final paycheck = 75000*1.02^40 = | $ 1,65,602.97 |

Value of the final paycheck = 165602.97/1.1^40 = | $ 3,658.99 |

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