SOLUTION: Suppose $1000 dollars is invested at an interest rate r. compounded continuously. If the balance grows to $1144.54 in 3 years. Find the time it will take for the balamce to grow to

Question 294557: Suppose $1000 dollars is invested at an interest rate r. compounded continuously. If the balance grows to $1144.54 in 3 years. Find the time it will take for the balamce to grow to $2500.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Suppose $1000 dollars is invested at an interest rate r. compounded continuously. If the balance grows to $1144.54 in 3 years. Find the time it will take for the balance to grow to $2500.
.
Continuous Compound Interest Formula
A = Pe^(rt)
where, P = principal amount (initial investment)
r = annual interest rate (as a decimal)
t = number of years
A = amount after time t
.
First, find the interest rate:
A = Pe^(rt)
1144.54 = 1000e^(r(3))
1144.54/1000 = e^(3r)
ln(1144.54/1000) = 3r
ln(1144.54/1000)/3 = r
.045 = r
.
Now, you can answer:
Find the time it will take for the balance to grow to $2500.
A = Pe^(rt)
2500 = 1000e^(.045t)
2500/1000 = e^(.045t)
ln(2500/1000) = .045t
ln(2500/1000)/.045 = t
20.36 years = t

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