Question 1209843
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.