Answer:
r = 3.45%
Step-by-step explanation:
You need the formula for continuously compounding interest, which is
A = Pe^(rt) , where
A is the total amount of money in the account,
P is the initial investment
e is a constant that represents continuous growth
r is the interst rate as a decimal (which we will be solving for)
t is how many years the interest was compounded
Plug in the given information
614.99 = 500e^(r6) (we need to solve for r)
614.99/500 = e^(6r) (divide both sides by 500, simplify the righ side)
1.22998 = e^(6r) (simpligy the left side)
When using 'e', we can take the natural log of both sides of the equation and use rules for logarithms to simplify further...
ln (1.22998) = ln (e^(6r)
ln (1.222998) = (6r)(ln e) (exponent rule for natural logs lets us bring
down any exponents as multipliers
ln (1.22998) = 6r (ln e = 1, you can verify this on your calculator)
ln (1.22998)/6 = r (divide both sides by 6 to isolate r)
.034499652 = r (Use a calculator to simplify the left side)
We need to write r as a percent, rounded to the nearest hundredth, so multiply r by 100%, then round
(0.034499652)(100%) = 3.4499652%
Rounding gives 3.45%
