SOLUTION: you invest P dollars in an account that compounds monthly. how long will it take for the account to double to 2P dollars if the annual interest rate is the following. solve using l
Algebra.Com
Question 368568: you invest P dollars in an account that compounds monthly. how long will it take for the account to double to 2P dollars if the annual interest rate is the following. solve using logarithms.
2%
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The formula for the Future Value, 
, of an investment 
at interest rate, 
, percent per annum compounded 
times per annum for 
years is:
^{mt})
Since you want your investment to double, 
, hence:
^{12t}\ =\ 2)
And we need to solve for . The first thing to do is use the Rule of 72 in your head to get an approximation of the answer so that you make sure your answer is at least reasonable. Divide 72 by the interest rate to get an approximation of the time it takes an investment to double: 36 years in this case.
Simplify inside the parentheses and then take the natural log of both sides:
^{12t}\ =\ \ln(2))
Use the rules of logs:
\ =\ n\log_b(x))
to write:
\ =\ \ln(2))
Then solve for :
}{12\ln\left(1.001\overline{6}\right)})
The rest is just poking fun at your calculator.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
If you deposit 500 dollars into an account earning 7.8 percent interest compounded... (answered by General_Lee87)
Ten thousand dollars is deposited in an account that pays 6% annual interest. How long... (answered by solver91311,greenestamps)
you deposit $3000 in a savings account that pays 5% annual interest. if the account... (answered by Alan3354)
If $5530 is invested in an account at 5% interest compounded monthly, how long will it... (answered by Boreal)
If You deposit money into an account that pays 4.5% annual interest. If the account is... (answered by Alan3354)
If you invest a sum of money in an account earning 12% annual interest, how long will it... (answered by rfer)
If you deposit P dollars into a bank account paying an annual interest rate r, (expressed (answered by EMStelley)
Suppose you invest $3000 in an account that pays 5.9% interest compounded continuously;... (answered by vleith)
8000 dollars in my saving account that give me 2.6% interest compunded conituously how... (answered by Gogonati)
