ces Complete the following without using Table12.1. Note: Round the "Total amount" and "Total interest" to the nearest cent. Principal $ 1,350 Time (years) Rate of compound interest Compounded Periods 8 % Quarterly 2 Rate % Total amount Total interest
ces Complete the following without using Table12.1. Note: Round the "Total amount" and "Total interest" to the nearest cent. Principal $ 1,350 Time (years) Rate of compound interest Compounded Periods 8 % Quarterly 2 Rate % Total amount Total interest
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Complete the fol
![Complete the following without using Table 12.1.
**Note:** Round the "Total amount" and "Total interest" to the nearest cent.
| Principal | Time (years) | Rate of compound interest | Compounded | Periods | Rate | Total amount | Total interest |
|-----------|--------------|---------------------------|------------|--------|------|--------------|---------------|
| $1,350 | 1 | 8% | Quarterly | | | | |
In this table, a principal amount of $1,350 is invested for 1 year at a compound interest rate of 8% per annum, compounded quarterly. The columns for "Periods", "Rate", "Total amount", and "Total interest" are to be completed.
The "Periods" column indicates the number of times the interest is compounded within a year. Since it's compounded quarterly, there are 4 periods in a year.
The "Rate" column reflects the interest rate applied in each period. It is calculated by dividing the annual rate (8%) by the number of periods (4), resulting in a rate of 2% per quarter.
The last two columns "Total amount" and "Total interest" are to be calculated based on the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = Total amount after time \( t \)
- \( P \) = Principal amount ($1,350)
- \( r \) = Annual nominal interest rate (8% or 0.08)
- \( n \) = Number of compounding periods per year (4)
- \( t \) = Time in years (1)
After calculating "Total amount", "Total interest" is found by subtracting the principal from "Total amount". Both results should be rounded to the nearest cent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce68a1d7-2c9d-42c0-910f-e97ed1de67c3%2F22a1d255-2345-40cb-98f5-e4538419f285%2Fgwihbet_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Complete the following without using Table 12.1.
**Note:** Round the "Total amount" and "Total interest" to the nearest cent.
| Principal | Time (years) | Rate of compound interest | Compounded | Periods | Rate | Total amount | Total interest |
|-----------|--------------|---------------------------|------------|--------|------|--------------|---------------|
| $1,350 | 1 | 8% | Quarterly | | | | |
In this table, a principal amount of $1,350 is invested for 1 year at a compound interest rate of 8% per annum, compounded quarterly. The columns for "Periods", "Rate", "Total amount", and "Total interest" are to be completed.
The "Periods" column indicates the number of times the interest is compounded within a year. Since it's compounded quarterly, there are 4 periods in a year.
The "Rate" column reflects the interest rate applied in each period. It is calculated by dividing the annual rate (8%) by the number of periods (4), resulting in a rate of 2% per quarter.
The last two columns "Total amount" and "Total interest" are to be calculated based on the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = Total amount after time \( t \)
- \( P \) = Principal amount ($1,350)
- \( r \) = Annual nominal interest rate (8% or 0.08)
- \( n \) = Number of compounding periods per year (4)
- \( t \) = Time in years (1)
After calculating "Total amount", "Total interest" is found by subtracting the principal from "Total amount". Both results should be rounded to the nearest cent.
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