how long does it take for a deposit of $1400 to double at 7% compounded continously
it would be awesome if you could also tell me how to do it...
Pt = Po*e^rt.
Pt = 1400*e^rt = 2800,
1400*e^rt = 2800,
Divide both sides by 1400:
e^rt = 2,
Take ln of both sides:
rt*lne = ln2,
Divide both sides by lne & get:
rt = ln2 / lne,
lne = 1,
rt = ln2 / 1,
rt = 0.6931,
0.07t = 0.6931,
t = 0.6931 / 0.07 = 9.902 Years.
To calculate how long it takes for a deposit to double at a given interest rate when compounded continuously, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial deposit)
e = Euler's number (approximately 2.71828)
r = the annual interest rate (in decimal form)
t = the time period (in years)
In this case, we want to find the time it takes for $1400 to double at a 7% interest rate. Let's solve for t:
$2800 = $1400 * e^(0.07t)
Divide both sides by $1400:
2 = e^(0.07t)
Take the natural logarithm of both sides:
ln(2) = ln(e^(0.07t))
ln(2) = 0.07t
Divide both sides by 0.07:
t = ln(2) / 0.07
Using a calculator, you can find that ln(2) is approximately 0.6931. Substitute this value into the equation:
t ≈ 0.6931 / 0.07 ≈ 9.9 years
Therefore, it takes approximately 9.9 years for a deposit of $1400 to double at a 7% interest rate when compounded continuously.
To calculate the time it takes for a deposit to double with continuous compounding, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Final amount (double the initial deposit)
P = Principal amount (initial deposit)
e = Euler's number, approximately 2.71828
r = Annual interest rate (written as a decimal)
t = Time in years
In this case, you want to find the time it takes for $1400 to double at a 7% interest rate. Let's solve for t:
2P = P * e^(0.07t)
Divide both sides of the equation by P:
2 = e^(0.07t)
Take the natural logarithm (ln) on both sides:
ln(2) = 0.07t
Divide both sides of the equation by 0.07:
t = ln(2) / 0.07
Now you can solve for t using a calculator:
t ≈ ln(2) / 0.07
t ≈ 9.906
Therefore, it will take approximately 9.906 years for a deposit of $1400 to double at a 7% interest rate with continuous compounding.
Remember to round the answer to an appropriate number of decimal places based on the level of accuracy required for your calculation.