Suppose you have borrowed $15,300 for school expenses at 7% simple interest for 6 years. Part 1 of 4 (a) How much simple interest would you pay? After 6 years, you would pay $ 6426 in simple interest. Part: 1 / 4 Part 2 of 4 (b) Suppose the bank splits the loan into six 1-year loans, so that the future value of the loan would be recalculated at the end of each one-year period, with interest charged on the new amount for the next year. Fill in the following table, which will show the future value of the loan at the end of each 1-year period. Round to the nearest dollar. End of Year Future Value, $ 1 ■ 2 3 4 5 n 6 ☐ X
Suppose you have borrowed $15,300 for school expenses at 7% simple interest for 6 years. Part 1 of 4 (a) How much simple interest would you pay? After 6 years, you would pay $ 6426 in simple interest. Part: 1 / 4 Part 2 of 4 (b) Suppose the bank splits the loan into six 1-year loans, so that the future value of the loan would be recalculated at the end of each one-year period, with interest charged on the new amount for the next year. Fill in the following table, which will show the future value of the loan at the end of each 1-year period. Round to the nearest dollar. End of Year Future Value, $ 1 ■ 2 3 4 5 n 6 ☐ X
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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After finding the value of the six one year loans,
![### Understanding Simple Interest and Compound Interest with an Example Loan
Suppose you have borrowed $15,300 for school expenses at 7% simple interest for 6 years.
#### Part 1: Calculating Simple Interest
**(a) How much simple interest would you pay?**
- After 6 years, you would pay $6,426 in simple interest.
This can be calculated using the formula for simple interest:
\[ \text{Simple Interest} = P \times r \times t \]
Where:
- \( P \) is the principal amount ($15,300),
- \( r \) is the annual interest rate (7% or 0.07),
- \( t \) is the time period in years (6).
\[ 15,300 \times 0.07 \times 6 = 6,426 \]
#### Part 2: Exploring Compound Interest by Annual Recalculation
**(b) Suppose the bank splits the loan into six 1-year loans, so that the future value of the loan would be recalculated at the end of each one-year period, with interest charged on the new amount for the next year. Fill in the following table, which will show the future value of the loan at the end of each 1-year period. Round to the nearest dollar.**
The table below illustrates the recalculated future value of the loan for each year:
| End of Year | 1 | 2 | 3 | 4 | 5 | 6 |
|-------------|--------|--------|--------|--------|--------|--------|
| Future Value, \$ | \[\] | \[\] | \[\] | \[\] | \[\] | \[\] |
To calculate the future value for each year:
\[ \text{Future Value}_{n} = \text{Principal} \times (1 + r)^n \]
Where:
- \( n \) is the year number.
1. **Year 1:**
\[ \text{Future Value}_1 = 15,300 \times (1 + 0.07)^1 = 15,300 \times 1.07 = 16,371 \]
2. **Year 2:**
\[ \text{Future Value}_2 = 16,371 \times (1 + 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf54cc92-fe70-42ec-a5a5-6c03b8447a69%2F03efd2fe-9ad2-4a46-8c46-d396d46dd932%2Fxr2bcup_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Simple Interest and Compound Interest with an Example Loan
Suppose you have borrowed $15,300 for school expenses at 7% simple interest for 6 years.
#### Part 1: Calculating Simple Interest
**(a) How much simple interest would you pay?**
- After 6 years, you would pay $6,426 in simple interest.
This can be calculated using the formula for simple interest:
\[ \text{Simple Interest} = P \times r \times t \]
Where:
- \( P \) is the principal amount ($15,300),
- \( r \) is the annual interest rate (7% or 0.07),
- \( t \) is the time period in years (6).
\[ 15,300 \times 0.07 \times 6 = 6,426 \]
#### Part 2: Exploring Compound Interest by Annual Recalculation
**(b) Suppose the bank splits the loan into six 1-year loans, so that the future value of the loan would be recalculated at the end of each one-year period, with interest charged on the new amount for the next year. Fill in the following table, which will show the future value of the loan at the end of each 1-year period. Round to the nearest dollar.**
The table below illustrates the recalculated future value of the loan for each year:
| End of Year | 1 | 2 | 3 | 4 | 5 | 6 |
|-------------|--------|--------|--------|--------|--------|--------|
| Future Value, \$ | \[\] | \[\] | \[\] | \[\] | \[\] | \[\] |
To calculate the future value for each year:
\[ \text{Future Value}_{n} = \text{Principal} \times (1 + r)^n \]
Where:
- \( n \) is the year number.
1. **Year 1:**
\[ \text{Future Value}_1 = 15,300 \times (1 + 0.07)^1 = 15,300 \times 1.07 = 16,371 \]
2. **Year 2:**
\[ \text{Future Value}_2 = 16,371 \times (1 + 0
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