SOLUTION: How long do you need to invest your money in an account earning an annual interest rate of 5,624% compounded daily so that your investment grows from $1380.96 to $10369 over that

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Question 1209843: How long do you need to invest your money in an account earning an annual interest rate of 5,624% compounded daily so that your investment grows from $1380.96 to $10369 over that period of time? give answer in days
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
Let's break down how to calculate the investment time.
**Understanding the Problem**
* We have an initial investment (principal) of $1380.96.
* We want the investment to grow to $10369.
* The annual interest rate is 5,624% (which is 56.24 as a decimal), compounded daily.
**Using the Compound Interest Formula**
The formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
* A = the future value of the investment/loan, including interest
* P = the principal investment amount (the initial deposit or loan amount)
* r = the annual interest rate (decimal)
* n = the number of times that interest is compounded per year
* t = the number of years the money is invested or borrowed for
In this case:
* A = $10369
* P = $1380.96
* r = 56.24
* n = 365 (compounded daily)
* t = ?
We need to solve for t.
1. **Rearrange the formula to solve for t:**
* t = log(A/P) / (n * log(1 + r/n))
2. **Plug in the values:**
* t = log(10369 / 1380.96) / (365 * log(1 + 56.24 / 365))
3. **Calculate the result:**
* t ≈ 35.85 years
4. **Convert years to days:**
* 35.85 years * 365 days/year ≈ 13085 days
**Answer**
You would need to invest your money for approximately 13085 days.
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
How long do you need to invest your money in an account earning an annual interest rate of 5,624%
compounded daily so that your investment grows from $1380.96 to $10369 over that period of time?
give answer in days
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 


The formula for the future value of the deposit compounded daily is

    FV = ,

where n is the number of days.  So we write

    10369 = .


Divide both sides by  1380.96

     = .


Simplify

    7.50854478 = .


Take logarithm of both sides

    log(7.50854478) = 


Express n  and calculate

    n =  = 13085.2 days.


Round it to the closest greater day.


ANSWER.  13086 days.

Solved.



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