SOLUTION: Edit: I forgot to add that college costs $169,208 for 4 years I have to use the formula A = P e^rt where t=18, r = 4%. How old will a person be if their parents invested $5000

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Edit: I forgot to add that college costs $169,208 for 4 years I have to use the formula A = P e^rt where t=18, r = 4%. How old will a person be if their parents invested $5000       Log On

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Question 593251: Edit: I forgot to add that college costs $169,208 for 4 years
I have to use the formula A = P e^rt where t=18, r = 4%. How old will a person be if their parents invested $5000 when they were born at an interest rate of 4%. I'm trying to figure out what the balance in the account will be when the person is 18 to see if there is enough to pay for college. If not, then I have to figure out how old I will be when enough money is available....using logs. I don't know how to set up the problem using logs.
Answer by jim_thompson5910(28536) About Me  (Show Source):
You can put this solution on YOUR website!
First off, let's see if investing $5,000 at a rate of 4% a year (for 18 years) will give us $169,208

A+=+Pe%5E%28rt%29

A+=+5000%2Ae%5E%280.04%2A18%29

A+=+5000%2Ae%5E%280.72%29

A+=+5000%2A2.05443321064389

A+=+10272.1660532194

So investing $5,000 at a rate of 4% for 18 years will give you $10,272.17

This is far below the target goal of $169,208
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Now let's see how long it will take for $5,000 to grow into $169,208 given it's growing at a rate of 4% each year.

A+=+Pe%5E%28rt%29

169208+=+5000%2Ae%5E%280.04t%29

169208%2F5000+=+e%5E%280.04t%29

33.8416+=+e%5E%280.04t%29

ln%2833.8416%29+=+ln%28e%5E%280.04t%29%29

ln%2833.8416%29+=+0.04t%2Aln%28e%29

ln%2833.8416%29+=+0.04t%2A%281%29

ln%2833.8416%29+=+0.04t

ln%2833.8416%29%2F0.04+=+t

3.52169081494417%2F0.04+=+t

88.0422703736043+=+t

t+=+88.0422703736043


So it will take roughly 88.04 years (so a little over 88 years) to accumulate $169,208

This is a very very long long time and by the time you do receive the money you were looking for, you may not be around to collect or use it.

So you either need to invest more (increase the value of P) or increase the rate of growth r. Of course, a combination of the two works as well.
More than likely, you'll have to increase the value of P significantly as you'll have more control over that compared to the interest rate r.