If 3000 dollars is invested in a bank account at an interest rate of 10 percent per year, Find the amount in the bank after 8 years if interest is compounded annually: Find the amount in the bank after 8 years if interest is compounded quarterly: Find the amount in the bank after 8 years if interest is compounded monthly: Finally, find the amount in the bank after 8 years if interest is compounded continuously:
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.
![### Investment Growth Calculation
If $3000 is invested in a bank account at an interest rate of 10 percent per year, discover how much your investment will grow under different compounding frequencies.
1. **Find the amount in the bank after 8 years if interest is compounded annually:**
Input the final amount in the box below:
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2. **Find the amount in the bank after 8 years if interest is compounded quarterly:**
Input the final amount in the box below:
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3. **Find the amount in the bank after 8 years if interest is compounded monthly:**
Input the final amount in the box below:
```
[____________________________]
```
4. **Finally, find the amount in the bank after 8 years if interest is compounded continuously:**
Input the final amount in the box below:
```
[____________________________]
```
After inputting the appropriate values, click the button below to check your answers:
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[Check Answer]
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### Formulae for Reference:
- **Annually Compounded Interest:**
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where \(A\) is the amount, \(P\) is the principal ($3000), \(r\) is the annual interest rate (10% or 0.10), \(n\) is the number of times interest is compounded per year (1 for annually), and \(t\) is the time in years (8 years).
- **Quarterly Compounded Interest:**
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where \(n\) is 4 for quarterly compounding.
- **Monthly Compounded Interest:**
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where \(n\) is 12 for monthly compounding.
- **Continuously Compounded Interest:**
\[
A = P e^{rt}
\]
where \(e\) is the base of the natural logarithm (approximately equal to 2.71828).
Use these equations to calculate the desired amounts for each scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13ec9e06-9a78-4a6f-8a7c-4a2195627caf%2Fd2af10db-b83e-4417-ad5c-3bf91956059f%2Fchgp4l_processed.jpeg&w=3840&q=75)
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