Uncle Fred recently died and left $305,000 to his 50-year-old favorite niece. She immediately spent $90,000...

Uncle Fred recently died and left $305,000 to his 50-year-old favorite niece. She immediately spent $90,000 on a town home but decided to invest the balance for her retirement at age 65. What rate of return must she earn on her investment over the next 15 years to permit her to withdraw $70,000 at the end of each year through age 80 if her funds earn 8 percent annually during retirement? Round your answer to the nearest whole number.

Solutions

Expert Solution

Money received by the Niece= $305,000

Money spent= $90,000

Money remaining= $(305,000-90,000)= $215,000

The neice only has $215,000.

The niece wants to earn an annuity of $70,000 per year for 15 years at an interest of 8% per year, thus we first need to know what amount of money she would need to invest in her retirement to get $70,000 per year. For that we will use the formula here C is the annuity=$70,000, i is the interest rate= 8% and n is the period of annuity=15

Thus by substituting the value we get=

on solving this equation you will get =

further solving it will give you = 70000*8.56= $599,163.51

ALTERNATE OPTION- you may alternatively use excel's PV function and put the values as rate=0.08, nper=15, PMT=70,000, FV=0 and press enter. You will get the same answer in negative due to some error in excel,but you can convert it to positive on your own.

The total money she needs at the time of her retirement is $599,163.51.

Currently she has $215,000, thus we now need to know in what rate of interest she should invest this money to have $599,163.51 in 15 years when she will retire. For this you may use a financial calculator or EXCEL

Use the Rate function in the excel and put nper=15, PMT=0, PV=-215,000 (you need to put this in negative because of some error in excel) and FV= $599,163.51.

The rate she would need to invest $215,000 to get an annuity of $70,000 for 15 years from her retirement is 7.07% or 7% as the question asks us to round it off to a whole number.

jeff jeffy answered 2 hours ago

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