Calculate the length of time for 800000 mirror to 15000 a invested at 10% per annum explain further

Answer 1

To calculate the length of time it takes for an investment of 800,000 (let's assume currency units) to grow to 15,000 (but it seems like there might be a typo, as usually an investment grows by compounding rather than being less after growth) at an interest rate of 10% per annum, we can assume you are asking how long it would take for 800,000 to grow to a certain amount through compounding.

Let's clarify first that with simple interest you would not see a case where the final amount is less than the principal unless the investment is paid out in installments or there is some sort of loss. However, for educational purposes, we can calculate how long it would take for an investment to grow with the compounding interest formula.

The formula for compound interest is:

\[ A = P(1 + r)^t \]

Where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (the initial amount of money).
• \( r \) is the annual interest rate (decimal).
• \( t \) is the time the money is invested or borrowed for, in years.

If we rearrange this to find \( t \):

\[ t = \frac{\log(A/P)}{\log(1 + r)} \]

Assuming we meant to calculate how long it takes for 800,000 to reach 15,000, though that seems unrealistic in the growth context (instead, if you're looking for how long it'll take to reach a higher amount), here’s how it would be done assuming you meant a higher amount:

Example Calculation

If instead, you want to know how long it takes to grow 800,000 to a higher end like, say, 1,000,000, this would be:

1. Given values:

   • \( P = 800,000 \)
   • \( A = 1,000,000 \)
   • \( r = 10% = 0.10 \)

2. Plug values into formula: \[ t = \frac{\log(1,000,000/800,000)}{\log(1 + 0.10)} \]

   \[ t = \frac{\log(1.25)}{\log(1.10)} \]

3. Calculating that:

   • \( \log(1.25) \approx 0.09691 \)
   • \( \log(1.10) \approx 0.04139 \)

   \[ t = \frac{0.09691}{0.04139} \approx 2.34 \text{ years} \]

Conclusion

Thus, it would take approximately 2.34 years for an investment of 800,000 to grow to 1,000,000 at an interest rate of 10% compounded annually.

If you meant something different with your initial amounts, please clarify, and I will adjust the response accordingly!