Question 1000216: Please help me solve this word problem:
An investor wants to have a retirement nest egg $100,000 and estimates that her investment now will grow at 4% compounded continuously for 30 years. What amount should she invest now to achieve this goal? (do not approximate until your final answer.)
Thank you so much.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Formula Used:
A = P*e^(r*t)
Given values:
A = 100,000
r = 0.04
t = 30
What we want to find: P
The goal is to solve for P. In other words, isolate P on its own side.
Note: 'e' is the constant 2.718... It's a lot like pi = 3.14... in that it is a decimal value that goes on forever without any fixed pattern.
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A = P*e^(r*t)
100,000 = P*e^(0.04*30) ... plug in the given values (see above)
100,000 = P*e^(1.2)
100,000 = P*3.32011692
100,000/3.32011692 = P*3.32011692/3.32011692 ... Divide both sides by 3.32011692.
30,119.4212160457 = P
P = 30,119.4212160457
P = 30,119.42
So you need to invest $30,119.42
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