Finance. Suppose that $ 4,600 is invested at 5.6 % annual interest​ rate, compounded monthly. How much money will be in the account in​ (A) 10 ​months? (B) 18 ​years?

To solve this, we can use the formula for compound interest:

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

Where:
- $A$ is the amount of money in the account after time $t$,
- $P$ is the principal (initial investment),
- $r$ is the annual interest rate (in decimal form),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the time in years.

### Given:
- $P = 4600$ (the initial investment),
- $r = 5.6\% = 0.056$ (the annual interest rate),
- $n = 12$ (since the interest is compounded monthly),
- $t$ is different for each part of the question.

### (A) For 10 months:

Since $t$ needs to be in years, $t = \frac{10}{12} = \frac{5}{6}$ years.

Now we substitute the values into the formula:

\[
A = 4600 \left(1 + \frac{0.056}{12}\right)^{12 \times \frac{5}{6}}
\]

### (B) For 18 years:

Here, $t = 18$ years.

Substituting these values into the formula:

\[
A = 4600 \left(1 + \frac{0.056}{12}\right)^{12 \times 18}
\]

Let's calculate the final amounts for both cases.### Results:
- **(A)** After 10 months, the amount in the account will be approximately **$4,819.23**.
- **(B)** After 18 years, the amount in the account will be approximately **$12,575.01**.

Would you like more details or have any questions? Here are five related questions you might find useful:

1. How does the frequency of compounding (monthly, annually, etc.) affect the final amount?
2. What would the result be if the interest was compounded quarterly instead of monthly?
3. How does changing the interest rate affect long-term growth in an account like this?
4. How can you determine how long it will take for an investment to double at a given interest rate?
5. What is the difference between compound interest and simple interest in long-term investments?

**Tip:** Always check the compounding frequency when evaluating the growth of investments, as it significantly impacts the final amount.

Suppose that $4,600 is invested at 5.6% annual interest rate, compounded monthly. How much money will be in the account in (A) 10 months? (B) 18 years?

Learn how to calculate compound interest for an initial investment of $4,600 at a 5.6% annual interest rate, compounded monthly. See how much money will be in the account after 10 months and 18 years using the compound interest formula. This guide is suitable for students in Grades 10-12.

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