SOLUTION: Matt decided to invest $800 in an account and was able to take out $920 from the account after 8 years. The interest in the account was compounded continuously. What was the inter

Question 1147499: Matt decided to invest $800 in an account and was able to take out $920 from the account after 8 years. The interest in the account was compounded continuously. What was the interest rate for his account?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula to use is f = p * e ^ (r * t)
f is the future value
p is the present value
r is the interest rate per time period
t is the number of time peiods

formula becomes 920 = 800 * e ^ (r * 8)
divide both sides of this equation by 800 to get:
920 / 800 = e ^ (r * 8)
take the natural log of both sides of this equation to get:
ln(920/800) = ln(e ^ (r * 8))
since ln(e ^ (r * 8)) is equivalent to r * 8 * ln(e), and since ln(e) is equal to 1, then the formula becomes:
ln(920/800) = r * 8
divide both sides of this equation by 8 to get:
ln(920/800)/8 = r
solve for r to get:
r = .0174702428
confirm by replacing r with that in the original equation to get:
920 = 800 * e ^ ( .0174702428 * 8)
this becomes 920 = 920, confirming the value for r is correct.
the continuous compounding interest rate is .0174702428 = 1.74702428%.

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