Question

(Future value) Sarah Wiggum would like to make a single lump-sum investment and have $1.6 million at the time of her retirement in 30 years. She has found a mutual fund that expects to earn 7 percent annually. How much must Sarah invest today? If Sarah earned an annual return of 15 percent, how much must she invest today?

a. If Sarah can earn 7 percent annually for the next 30 years, how much will she have to invest today? $_________(Round to the nearest cent)

Answer 1

To Solve this Question we need to apply formula of Compound Amount and by putting values given in the question we can find out Principal Amount ( Today's Investment ):

Formula :

CA = P (1+r)ⁿ

Where, CA = Compound Amount (Future Value)

P = Principal Amount or Initial Investment

r = Rate of Return

n = Time period (No. of years)

(A) : If Sarah can earn 7 percent annually for the next 30 years the amount she have to invest today is as follows:

CA = P (1+r)ⁿ

$1600000 = P(1+0.07)³⁰

$1600000 = P(7.612255)

P = $1600000 / 7.612255

P = $210187.39 or $ 0.21 million

Therefore she need to invest $210187.39 or $ 0.21 million today to receive $ 1.6 million after 30 years at 7% interest annualy.

(B) :If Sarah can earn 15 percent annually for the next 30 years the amount she have to invest today is as follows:

CA = P (1+r)ⁿ

$1600000 = P(1+0.15)³⁰

$1600000 = P(66.211772)

P = $1600000 / 66.211772

P = $24165.89 or $ 0.024 million

Therefore she need to invest $24165.89 or $ 0.024 million today to receive $ 1.6 million after 30 years at 15% interest annualy.