you deposit 8500 dollars in an account that pays you 3.5 % interest compounded continuously. How long will it take for the money to triple?
3 = 1(e^.035t)
ln 3 = .035t lne
t = ln3/.035 = 31.4 years
p = Po e^(.035 t)
3 = e^(.035 t)
ln 3 = .035 t
1.0986 = .035 t
t = 31.4 years
To determine how long it will take for the money to triple, we can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A = the final amount (triple the initial amount, in this case)
P = the initial deposit
e = the mathematical constant approximately equal to 2.71828
r = the interest rate
t = time in years
In this case, we have:
P = $8500
A = $8500 * 3 = $25500
r = 3.5% = 0.035
Plugging these values into the formula, we get:
$25500 = $8500 * e^(0.035t)
Now we need to solve for t. Divide both sides by $8500:
3 = e^(0.035t)
Next, take the natural logarithm of both sides to isolate the exponent:
ln(3) = ln(e^(0.035t))
Simplify using the property of logarithms:
ln(3) = 0.035t * ln(e)
Since ln(e) is equal to 1:
ln(3) = 0.035t
Now, divide both sides by 0.035:
t = ln(3) / 0.035
Using a calculator, we find:
t ≈ 19.95
Therefore, it would take approximately 19.95 years for the money to triple.
To determine how long it will take for the money to triple, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the future value or amount after time t
P is the principal amount (initial deposit)
e is the mathematical constant approximately equal to 2.71828
r is the interest rate
t is the time period in years
In this case, we need to find the time period (t) when the future value (A) is three times the principal amount (P).
Let's set up the equation:
3P = P * e^(0.035t)
Divide both sides of the equation by P:
3 = e^(0.035t)
Now, take the natural logarithm (ln) of both sides:
ln(3) = ln(e^(0.035t))
Since ln(e^x) = x, we can simplify further:
ln(3) = 0.035t
Now, divide both sides of the equation by 0.035:
t = ln(3) / 0.035
Using a calculator or math software, we can evaluate this expression:
t ≈ 19.82
Therefore, it will take approximately 19.82 years for the money to triple.