Find the final amount of money in an account if 38, 800 is deposited at 5 % interest compounded quarterly (every 3 months) and the money is left for 6 years. The final amount is $ Round answer to 2 decimal places Submit Question
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Compound Interest Calculation
**Problem Statement:**
Find the final amount of money in an account if $8,800 is deposited at 5% interest compounded quarterly (every 3 months) and the money is left for 6 years.
**Details:**
- Principal (P): $8,800
- Annual Interest Rate (r): 5% or 0.05
- Number of times interest is compounded per year (n): 4 (quarterly)
- Time the money is invested (t): 6 years
**Formula:**
The formula to calculate the final amount (A) with compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( P \) = initial principal balance
- \( r \) = annual interest rate (decimal)
- \( n \) = number of times interest applied per time period
- \( t \) = number of time periods the money is invested for
**Calculation Steps:**
1. Convert the annual interest rate from a percentage to a decimal by dividing by 100.
2. Plug the values into the compound interest formula.
3. Solve the equation to find the final amount.
#### Example:
- Convert the interest rate:
\( \frac{5}{100} = 0.05 \)
- Substitute into the formula:
\[ A = 8800 \left(1 + \frac{0.05}{4}\right)^{4 \times 6} \]
\[ A = 8800 \left(1 + 0.0125\right)^{24} \]
\[ A = 8800 \left(1.0125\right)^{24} \]
4. Calculate \( (1.0125)^{24} \).
5. Multiply the result by 8800.
**Answer Format:**
The final amount is \$ [Your Answer Here]
Please note that the answer should be rounded to 2 decimal places.
**Submit Button:**
- To calculate the final amount and check your answer, click the "Submit Question" button.
[Submit Question]
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**Note**: Explanations above assume familiarity with the concepts of interest rates, compounding periods, and basic algebra. Adjust explanations based on your educational audience's level of expertise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd884bfb-f597-4e0f-84ff-0bb4284fea4d%2F3fd0e855-a0cb-4e97-bd2d-0f267c334da0%2Fvj74f8v_processed.jpeg&w=3840&q=75)
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