SOLUTION: Please help me solve this:
How long does it take for an initial investment of $7,000 earning 5.58% interest, compounded continuously , to double? (First find the exact solution
Algebra.Com
Question 606717: Please help me solve this:
How long does it take for an initial investment of $7,000 earning 5.58% interest, compounded continuously , to double? (First find the exact solution and then round to two decimal places.)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Where 
is the future value, 
is the present value, i.e. the initial investment, 
is the base of the natural logarithms which is the limit of ^n)
as 
becomes large, 
is the annual interest rate expressed as a decimal, and 
is the number of years.
Regardless of the amount of the initial investment, in order for it to double, 
and therefore 
must equal 2.
Hence:
and solve for
Take the natural log of both sides. Actually, the log of any base will work and, given correct arithmetic, will provide the correct answer. However, since the equation involves , the arithmetic is greatly simplified by using the natural log.
\ =\ \ln(2))
Use
\ =\ n\,\cdot\,\log_b(a))
To write
\ =\ \ln(2))
Then use
\ =\ 1)
to write
)
and finally
}{r})
Just use your calculator to divide )
by the interest rate. Don't forget that the interest rate must be expressed as a decimal.
After that, toss the following into your financial formulas toolkit:
An initial investment of at an interest rate of compounded continuously will increase by a factor of 
in }{r})
years.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
How long does it take for an initial investment of $2,500, earning 6.18% interest,... (answered by fractalier)
Please help me solve this problem:
Using the formula for compound interest, A=P(1+i)^n (answered by solver91311)
How long will it take an investment of $2,000 to reach $3,000 if it is earning 4%... (answered by Boreal,ikleyn)
Please help me When interest is compounded continuously, the balance in an account after (answered by stanbon,jim_thompson5910)
I am stuck at this question, please help me.
How long will it take an investment of... (answered by stanbon)
How long does it take an investment of R10 000 to double if it is invested at 8%,... (answered by jorel1380)
How long will it take for $9900 to grow to $29,000 at an interest of 8.3% if interest is... (answered by stanbon)
How many years will it take for an initial investment of $10,000 to grow to $35,000?... (answered by ikleyn)
Kyle Invests in an account earning 4.75% interest compounded continuously. How long will... (answered by MathLover1)
