Ndiba invests a sum of money in a savings account with a fixed annual interest rate of 4.61% compounded yearly. After 6 years, the balance reaches $5,485.85. What was the amount of the initial investment?

To determine the initial investment amount $ P $, we will again use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Given that the interest is compounded yearly, $ n = 1 $, so the formula simplifies to:

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

Where:
- $ A = 5,485.85 $ (the amount after 6 years),
- $ r = 4.61\% = 0.0461 $ (annual interest rate),
- $ t = 6 $ years,
- $ n = 1 $ (since interest is compounded yearly).

Rearranging to solve for $ P $:

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

Let's substitute the values and calculate $ P $.The initial investment amount was approximately **$4,186.05**.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:
1. How would the initial investment change if the interest rate was 5%?
2. What would the balance be after 6 years if the initial investment was $5,000 instead?
3. How much interest did Ndiba earn over the 6 years?
4. What would happen to the final amount if the interest was compounded monthly instead of yearly?
5. How would the outcome differ if the investment period was extended to 10 years?

**Tip:** Understanding the difference between different compounding frequencies (yearly, monthly, etc.) can help you make more informed investment decisions.

Learn how to calculate the initial investment using the compound interest formula. Given an annual interest rate of 4.61% compounded yearly, after 6 years, the investment grew to $5,485.85. Understand the principles of compound interest and how to apply the formula effectively.

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