Sean's investment of $81,400.00 in a fund matured to $155,777.80 in 8 years. If the interest in the fund is compounded semi-annually, calculate the following rounded to two decimal places. (i) (1) % b. Nominal interest rate (j) (j) a. Periodic interest rate
Sean's investment of $81,400.00 in a fund matured to $155,777.80 in 8 years. If the interest in the fund is compounded semi-annually, calculate the following rounded to two decimal places. (i) (1) % b. Nominal interest rate (j) (j) a. Periodic interest rate
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Investment Compounding Calculation Example**
Sean's investment of $81,400.00 in a fund matured to $155,777.80 in 8 years. If the interest in the fund is compounded semi-annually, calculate the following rounded to two decimal places:
a. Periodic interest rate
\( \text{(i)}\; (i)\; \% \)
b. Nominal interest rate
\( \text{(j)}\; (j) \)
- **Formulas:**
To find the values required, we would use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
In this case:
- \( P = \$81,400.00 \)
- \( A = \$155,777.80 \)
- \( t = 8 \) years
- \( n = 2 \) (since the interest is compounded semi-annually)
From this, you can isolate \( r \) and solve to find the interest rates requested.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc31f934b-62b7-425c-8b5d-bfb0b333f649%2F52f9453c-41cb-4a35-b81f-57d3d5292e33%2F3k5zwjc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Investment Compounding Calculation Example**
Sean's investment of $81,400.00 in a fund matured to $155,777.80 in 8 years. If the interest in the fund is compounded semi-annually, calculate the following rounded to two decimal places:
a. Periodic interest rate
\( \text{(i)}\; (i)\; \% \)
b. Nominal interest rate
\( \text{(j)}\; (j) \)
- **Formulas:**
To find the values required, we would use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
In this case:
- \( P = \$81,400.00 \)
- \( A = \$155,777.80 \)
- \( t = 8 \) years
- \( n = 2 \) (since the interest is compounded semi-annually)
From this, you can isolate \( r \) and solve to find the interest rates requested.
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