1) Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $2,800 is deposited quarterly for 20 years at 5% per year FV = $
1) Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $2,800 is deposited quarterly for 20 years at 5% per year FV = $
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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![**Annuity Account Accumulation Calculation**
1. **Objective**: Calculate the future value (\(FV\)) in an annuity account given certain parameters. This involves end-of-period deposits with compounding occurring at the same intervals as the deposits.
**Problem Statement**:
- Amount deposited each period: $2,800
- Frequency of deposits: Quarterly
- Period of deposit: 20 years
- Annual interest rate: 5%
**Future Value Formula**:
\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]
Where:
- \(FV\) is the future value of the annuity
- \(P\) is the periodic deposit amount ($2,800)
- \(r\) is the periodic interest rate (annual rate/number of periods per year, so \(5\%/4\))
- \(n\) is the total number of periods (years \(\times\) periods per year, so \(20 \times 4\))
**Solution**: Calculate the future value using the formula and round the answer to the nearest cent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F567b405c-a8ec-4133-a9f4-1b3e3fcbb4f8%2Fa6f5d5e1-604d-4c51-8367-f85a98745414%2Fasmuv6a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Annuity Account Accumulation Calculation**
1. **Objective**: Calculate the future value (\(FV\)) in an annuity account given certain parameters. This involves end-of-period deposits with compounding occurring at the same intervals as the deposits.
**Problem Statement**:
- Amount deposited each period: $2,800
- Frequency of deposits: Quarterly
- Period of deposit: 20 years
- Annual interest rate: 5%
**Future Value Formula**:
\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]
Where:
- \(FV\) is the future value of the annuity
- \(P\) is the periodic deposit amount ($2,800)
- \(r\) is the periodic interest rate (annual rate/number of periods per year, so \(5\%/4\))
- \(n\) is the total number of periods (years \(\times\) periods per year, so \(20 \times 4\))
**Solution**: Calculate the future value using the formula and round the answer to the nearest cent.
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