Question

 Sarah Wiggum would like to make a single investment and have ​$1.8 million at the time of her retirement in 35years. She has found a mutual fund that will earn 7 percent annually. How much will Sarah have to invest​ today? If Sarah earned an annual return of 14 ​percent, how soon could she then​ retire?  

a.  If Sarah can earn 7 percent annually for the next 35 ​years, the amount of money she will have to invest today is ​$____(Round to the nearest​ cent.)

Answer 1

Sarah would like to have $1.8 million at her retirement in 35 years.

Calculating the Amount she have to Invest today:-

FutureValue Invested Amount(1 + r)"

where, r = Interest rate = 7%

n = no of years = 35

Future Value = 1800,000

1800,000 = Invested Amount(1 + 0.07)35

1800, 000 = Invested Amount * 10.6765814846

Invested Amount = $168,593.29

So, Amount sarah needs to invest today is $168,593.29

b). If sarah now earned Interest at 14% annually

Assuming, Invested amount and Future Value to be same to calculate the no of years would take Sarah to accumulate $1.8 million for retirement.

FutureValue Invested Amount(1 + r)"

where, r = Interest rate = 14%

n = no of years =

Invested Amount = $168,593.29

Future Value = 1800,000

10.6765814846 = {1+0.14)

Taking log on both sides,

Log(10.6765814846) = n*Log(1.14)

1.0284322190 = n*0.056904851

n = 18.07 years

So, Sarah could retire in 18.07 years

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