The principal P is borrowed at a simple interest rater for a period of time t. Find the loan's future value A, or the total amount due at time t. P=$6000, r=4.5%, t = 4 months The loan's future value is $. (Do not round until the final answer. Then round to the nearest cent as needed.)
The principal P is borrowed at a simple interest rater for a period of time t. Find the loan's future value A, or the total amount due at time t. P=$6000, r=4.5%, t = 4 months The loan's future value is $. (Do not round until the final answer. Then round to the nearest cent as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![The problem presented involves calculating the future value of a loan using simple interest. Here's a transcription of the text:
---
The principal \( P \) is borrowed at a simple interest rate \( r \) for a period of time \( t \). Find the loan’s future value \( A \), or the total amount due at time \( t \).
\( P = \$6000, \, r = 4.5\%, \, t = 4 \) months
---
The loan’s future value is \( \$ \_\_\_\_ \)
(Do not round until the final answer. Then round to the nearest cent as needed.)
---
To calculate the future value \( A \) using simple interest, we use the formula:
\[
A = P(1 + rt)
\]
Here, the interest rate should be converted to a decimal and the time should be in years:
- \( r = 0.045 \) (4.5% as a decimal)
- \( t = \frac{4}{12} \) (4 months as a fraction of a year)
Calculate:
\[
A = 6000 \times (1 + 0.045 \times \frac{4}{12})
\]
This provides the total amount due at the end of the loan period.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58402a47-f1ff-47ea-9009-84135bb68162%2F1dd7ba64-0616-4726-a070-24972d63e77c%2Fbbrud1b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented involves calculating the future value of a loan using simple interest. Here's a transcription of the text:
---
The principal \( P \) is borrowed at a simple interest rate \( r \) for a period of time \( t \). Find the loan’s future value \( A \), or the total amount due at time \( t \).
\( P = \$6000, \, r = 4.5\%, \, t = 4 \) months
---
The loan’s future value is \( \$ \_\_\_\_ \)
(Do not round until the final answer. Then round to the nearest cent as needed.)
---
To calculate the future value \( A \) using simple interest, we use the formula:
\[
A = P(1 + rt)
\]
Here, the interest rate should be converted to a decimal and the time should be in years:
- \( r = 0.045 \) (4.5% as a decimal)
- \( t = \frac{4}{12} \) (4 months as a fraction of a year)
Calculate:
\[
A = 6000 \times (1 + 0.045 \times \frac{4}{12})
\]
This provides the total amount due at the end of the loan period.
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