Uninhibited Growth Model. This is an example problem from the book and need help figuring it out?
a) If $3500 is invested in an account that pays 5% interest compounded continuously, how long will it take to grow to $7000.
b) How much money will the account be worth in 20 years.
http://www.onlinecalculatorfree.org/law-of-uninhibited-growth-calculator.html#.WsHVGDMh02w
I found this free calculator on-line.
I saw your question earlier in the day but was unable to help you.
As MsPi's webpage shows the general formula for continuous growth is
amount = principal e^(kt), where k is the perodic rate as a decimal and t is the number of periods (in most cases the period is in years, like in your question)
3500 e^(.05t) = 7000
e^(.05t) = 2
take ln of both sides and use your log rules
.05t (ln e) = ln 2
.05t = .693147...
t = appr 13.9 years
for the second part simply replace t = 20 in the formula
To solve both parts of the problem, we will use the Uninhibited Growth Model, also known as the continuous compound interest formula. The formula for continuously compounded interest is:
A = P * e^(rt)
Where:
A = the final amount (future value)
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period (in years)
Let's break down each part of the problem.
a) If $3500 is invested in an account that pays 5% interest compounded continuously, how long will it take to grow to $7000?
We want to find the time period, so we rearrange the formula to solve for t:
t = ln(A/P) / r
Plugging in the given values:
P = $3500
A = $7000
r = 5% = 0.05
t = ln(7000 / 3500) / 0.05
t = ln(2) / 0.05
t ≈ 13.86 years
Therefore, it will take approximately 13.86 years for the investment to grow from $3500 to $7000 at a 5% interest rate compounded continuously.
b) How much money will the account be worth in 20 years?
To find the amount after 20 years, we can use the formula directly:
A = P * e^(rt)
Plugging in the given values:
P = $3500
r = 5% = 0.05
t = 20 years
A = 3500 * e^(0.05 * 20)
A ≈ 3500 * e^1
A ≈ 3500 * 2.71828
A ≈ $9529.98
Therefore, the account will be worth approximately $9529.98 after 20 years.