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Dale takes out a loan of with a interest rate that is compounded semi-annually.
If he pays off the loan in 3 years, how much will he end up paying?
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.

Ask by Harmon Schwartz. in the United States
Jan 24,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Dale will pay a total of $12,415.47 after 3 years.

Solution

To determine the total amount Dale will pay off after 3 years on a loan of $8,000 with a 15.2% annual interest rate compounded semi-annually, follow these steps:

1. Understand the Compounding Terms

  • Principal §: $8,000
  • Annual Interest Rate ®: 15.2% or 0.152
  • Compounding Frequency: Semi-annually (twice a year)
  • Number of Years (t): 3

2. Calculate the Interest Rate per Period

Since the interest is compounded semi-annually:

3. Determine the Total Number of Periods

4. Use the Compound Interest Formula

The compound interest formula is:
Substituting the known values:

5. Calculate

First, compute the growth factor:

6. Calculate the Total Amount (A)

Multiply the principal by the growth factor:

7. Round to the Nearest Cent

Conclusion

Dale will end up paying $12,415.47 after 3 years.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

The Deep Dive

To calculate the total amount Dale will pay at the end of 3 years, we can use the formula for compound interest:
Where:
  • is the amount of money accumulated after n years, including interest.
  • is the principal amount (the initial amount of money).
  • is the annual interest rate (decimal).
  • is the number of times that interest is compounded per year.
  • is the number of years the money is borrowed.
Given:
  • (since interest is compounded semi-annually)
Now, plug in the values:
Calculate:
Therefore, Dale will end up paying approximately when he pays off the loan in 3 years.

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