Question 134074: If $10000 is invested at 6% compounded continously, in approximately how many years will the amount have grown to $15000? Answer by nycsharkman(136) (Show Source):
You can put this solution on YOUR website! We use the formula A = Pe^(rt)where
A = final balance
P = original investment
r = the annual interest rate (as a decimal)
t = investment time (in years)
e = a special "calculator number" that serves as the base of the
nalural logarithm.
Your question:
If $10000 is invested at 6% compounded continously, in approximately how many years will the amount have grown to $15000?
Let A = 15000
15000 = 10000e^(0.06t)
Divide both sides by 10000.
1.5 = e^(0.06t)
Rewrite as a log.
0.06t = In(1.5)
Solve for t.
t = In(1.5)/0.06
t = 6.757751802
Round 6.757751802 to the nearest ones place and we get
t is about 7 years.
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