please answer both questions. show work. thanks! Score: 0 of 4 pts 7 of 12 (12 c
ID: 1172418 • Letter: P
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please answer both questions. show work. thanks!
Score: 0 of 4 pts 7 of 12 (12 complete) HW Score: 68 33%, 34 17 of 50 i P5-12 (similar to) (Related to Checkpoint 5.4) (Present value) Sarah Wiggum would like to make a single investment and have $1.5 million at How much will Sarah have to invest today? If Sarah earned an annual retun of 14 percent, how soon could she then retire? a. If Sarah can earn 7 percent annually for the next 26 years, the amount of money she will have to invest today is s(Round to the nearest cent) E Question Help the time of her retirement in 26 years. She has found a mutual fund that will eam 7 percent annualy Enter your answer in the answer box and then click Check Answer O Type here to search ????.00 930 AMExplanation / Answer
Answer a.
Desired Amount = $1,500,000
Interest Rate = 7%
Time to Retirement = 26 years
Amount Invested = Desired Amount / (1 +Interest Rate)^Period
Amount Invested = $1,500,000 / (1 + 0.07)^26
Amount Invested = $1,500,000 / 1.07^26
Amount Invested = $258,293.24
So, Sarah has to invest $258,293.24 today in order to have $1,500,000 after 26 years
Answer b.
Desired Amount = $1,500,000
Amount Invested = $258,293.24
Interest Rate = 14%
Let time to retirement be ‘n’ years
Amount Invested * (1 +Interest Rate)^Period = Desired Amount
$258,293.24 * (1 + 0.14)^n = $1,500,000
$258,293.24 * 1.14^n = $1,500,000
1.14^n = 5.80735
n * ln(1.14) = ln(5.80735)
n = 13.43
So, Sarah can retire after 13.43 years if she can earn 14% annually.
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