marcia has $220,000 saved for her retirement. How long will it take for the investment to double in value if it earns 6% interest compounded continuously?
See http://www.moneychimp.com/articles/finworks/continuous_compounding.htm
for the exact answer (11.56 yrs), or use the "rule of 72*" and get about 12 years.
*The product of the annual interest rate and the number of years must be 72 to double your money.
i didn't get the right answer :[
the answer must be 139 months
In your case,
440000=220000*e^0.06t
2=e^0.06t
ln2 = 0.06t
t= ln2/0.06
= 11.5524 years x 12 months
=139 months
To find out how long it will take for the investment to double in value, we need to use the formula for continuous compound interest. The formula for continuous compound interest is:
A = P * e^(rt)
Where:
A = the final amount/ value
P = the initial investment/ principal amount
e = Euler's number (approximately 2.71828)
r = interest rate per period
t = time (in years)
In this case, the initial investment (P) is $220,000, and we want to find t, the time it takes for the investment to double.
The final amount (A) would be 2 times the initial investment (P), so A = 2P.
Substituting these values into the formula, we get:
2P = P * e^(rt)
To simplify the equation, we can divide both sides by P:
2 = e^(rt)
To isolate t, we can take the natural logarithm (ln) of both sides:
ln(2) = rt
Now we can solve for t by dividing both sides by r:
t = ln(2) / r
Plugging in the values, the interest rate (r) is 6% or 0.06 (in decimal form), so:
t = ln(2) / 0.06
Using a calculator or math software, we can find the natural logarithm of 2 and divide it by 0.06 to get the time it will take for the investment to double in value.