SOLUTION: Mario invest $280 at 8% interest compounded continuously. Write the exponential function to represent the situation and at what time will the total reach $1,000,000

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Question 1172129: Mario invest $280 at 8% interest compounded continuously. Write the exponential function to represent the situation and at what time will the total reach $1,000,000
Found 2 solutions by Boreal, math_helper:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
1000000=280^e^(rt)=280e^0.08t
3571.43=e^0.08t
don't round
ln both sides
0.08t=102.26 years
rule of 72, doubling time predicted to be 9 years
This is more than 11 doubling times

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


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


r = rate
t = time
P = Principal
F = Future value


+1000000+=+280e%5E%280.08t%29+

+1000000%2F280+=+e%5E%280.08t%29+

+ln%281000000%2F280%29+=+0.08t+

+8.180721+=+0.08t+

+t+=+8.180721%2F0.08+ = +102.26+ years

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That's a long time to wait.


If a person can put in $2,000 at the start, and then $2000 each year, they would have more than $1,000,000 after 46 years, assuming 8% return per year.