Juan invested $5,600 at 5.75% compounded quarterly for 7.5 years. How much will be in his account at the end of the time?(Round your answers to the nearest cent.)
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 Calculation: Compound Interest**
Juan invested $5,600 at an interest rate of 5.75% compounded quarterly for 7.5 years.
**Problem:** How much will be in his account at the end of the time period? (Round your answers to the nearest cent.)
[Input box for answers]
To solve this problem, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
For our specific problem:
- \( P = 5600 \)
- \( r = 5.75/100 = 0.0575 \)
- \( n = 4 \) (since the interest is compounded quarterly)
- \( t = 7.5 \)
Plugging these values into the formula:
\[ A = 5600 \left(1 + \frac{0.0575}{4}\right)^{4 \times 7.5} \]
\[ A = 5600 \left(1 + 0.014375\right)^{30} \]
\[ A = 5600 \left(1.014375\right)^{30} \]
Calculate the value inside the parentheses first:
\[ 1.014375^{30} \approx 1.5363 \]
Then multiply by the principal amount:
\[ A = 5600 \times 1.5363 \approx 8606.01 \]
Thus, at the end of 7.5 years, the amount in Juan's account will be approximately **$8606.01**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71316fb1-8245-4500-b615-2e27467e4912%2Fbca74882-157f-4132-b88a-5baee956a9b4%2Fdtifkan_processed.jpeg&w=3840&q=75)
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