2. Find the compound interest earned for $700 at 8% compounded semiannually for 4 years. A = P(I+5jnt %3D 957.9983 A = 100 (+:082X4) 2.2, %3D 700-000O A = 957.9983 257.9983 $258 compound interest earned rounded: $258
2. Find the compound interest earned for $700 at 8% compounded semiannually for 4 years. A = P(I+5jnt %3D 957.9983 A = 100 (+:082X4) 2.2, %3D 700-000O A = 957.9983 257.9983 $258 compound interest earned rounded: $258
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem:**
Find the compound interest earned for $700 at 8% compounded semiannually for 4 years.
**Solution:**
The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($700).
- \( r \) is the annual interest rate (8% or 0.08).
- \( n \) is the number of times that interest is compounded per year (2 for semiannual).
- \( t \) is the time the money is invested for in years (4).
**Calculation:**
\[ A = 700 \left(1 + \frac{0.08}{2}\right)^{2 \times 4} \]
\[ A = 700 \left(1 + 0.04\right)^8 \]
\[ A = 700 \times (1.04)^8 \]
After calculating, we find:
\[ A = 957.9983 \]
Next, calculate the compound interest earned:
\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 957.9983 - 700.0000 \]
\[ \text{Compound Interest} = 257.9983 \]
Rounded to the nearest dollar:
**Compound Interest Earned:**
\[ \boxed{258} \]
In summary, the compound interest earned is $258.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29b25716-5eb6-4537-b644-b049114aff43%2Ff64d5bf7-8eff-4410-8c95-1cb252827cd1%2Fytfb7u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the compound interest earned for $700 at 8% compounded semiannually for 4 years.
**Solution:**
The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($700).
- \( r \) is the annual interest rate (8% or 0.08).
- \( n \) is the number of times that interest is compounded per year (2 for semiannual).
- \( t \) is the time the money is invested for in years (4).
**Calculation:**
\[ A = 700 \left(1 + \frac{0.08}{2}\right)^{2 \times 4} \]
\[ A = 700 \left(1 + 0.04\right)^8 \]
\[ A = 700 \times (1.04)^8 \]
After calculating, we find:
\[ A = 957.9983 \]
Next, calculate the compound interest earned:
\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 957.9983 - 700.0000 \]
\[ \text{Compound Interest} = 257.9983 \]
Rounded to the nearest dollar:
**Compound Interest Earned:**
\[ \boxed{258} \]
In summary, the compound interest earned is $258.
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