How do I find the final amount of money in an account if $1900 is deposited at 3% interest compounded quarterly (every 3 months) and the money is left for 8 years? And, round the answer two decimal places?

To find the final amount of money in an account with compound interest, you can use the compound interest formula:

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

Where:
- $ A $ = the final amount in the account (what we're solving for)
- $ P $ = the principal amount (initial deposit) = \$1900
- $ r $ = annual interest rate (decimal) = $ \frac{3}{100} = 0.03 $
- $ n $ = number of times interest is compounded per year (quarterly, so $ n = 4 $)
- $ t $ = the number of years the money is left in the account = 8

Now we can plug in the values:

\[
A = 1900 \left(1 + \frac{0.03}{4}\right)^{4 \times 8}
\]

Let's calculate that step by step.

1. Calculate $ \frac{0.03}{4} $ = 0.0075
2. Add 1 to it: $ 1 + 0.0075 = 1.0075 $
3. Multiply $ n \times t $: $ 4 \times 8 = 32 $
4. Now raise $ 1.0075 $ to the 32nd power: $ (1.0075)^{32} $
5. Multiply that result by 1900 to get $ A $.

Let me calculate that for you.The final amount in the account after 8 years, with an initial deposit of \$1900 at 3% interest compounded quarterly, will be approximately **\$2413.21**.

Do you have any questions or would you like more details? Here are 5 related questions you might find helpful:

1. How would the final amount change if the interest rate increased to 5%?
2. What if the interest was compounded monthly instead of quarterly?
3. How much interest is earned over the 8-year period?
4. How does simple interest compare to compound interest for the same scenario?
5. What would the final amount be if the money was left for 10 years instead of 8?

**Tip:** The more frequently interest is compounded, the more interest accumulates over time.

How do I find the final amount of money in an account if $1900 is deposited at 3% interest compounded quarterly (every 3 months) and the money is left for 8 years? And, round the answer two decimal places?

Learn how to calculate the final amount in an account with $1900 deposited at 3% interest compounded quarterly for 8 years. This detailed guide explains how to use the compound interest formula to find the final balance, with step-by-step instructions. Suitable for high school students in Grades 9-12.

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