(Comprehensive problem) You would like to have $52,000 in 12 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 10 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 10 percent on this deposit) c. At the end of five years, you will receive $20,000 and deposit this in the bank toward your goal of $52,000 at the end of year 12. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 10 percent on your deposits.) a. How much must you deposit annually to accumulate this amount? $(Round to the nearest cent.) b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be? (Round to the nearest cent.) c. If you deposit $20,000 received at the end of five years in the bank, what will the amount grow to by the end of year 12? $(Round to the nearest cent.) In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? $(Round to the nearest cent.)
(Comprehensive problem) You would like to have $52,000 in 12 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 10 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 10 percent on this deposit) c. At the end of five years, you will receive $20,000 and deposit this in the bank toward your goal of $52,000 at the end of year 12. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 10 percent on your deposits.) a. How much must you deposit annually to accumulate this amount? $(Round to the nearest cent.) b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be? (Round to the nearest cent.) c. If you deposit $20,000 received at the end of five years in the bank, what will the amount grow to by the end of year 12? $(Round to the nearest cent.) In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? $(Round to the nearest cent.)
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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![## Comprehensive Problem
You would like to have $52,000 in 12 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 10 percent interest compounded annually. Your first payment will be made at the end of the year.
### Questions:
1. **How much must you deposit annually to accumulate this amount?**
- (Round to the nearest cent.)
2. **If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be?**
- (Assume you can earn 10 percent on this deposit.)
- (Round to the nearest cent.)
3. **If you deposit $20,000 received at the end of five years in the bank, what will the amount grow to by the end of year 12?**
- (Round to the nearest cent.)
4. **In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal?**
- (Again, assume you can earn 10 percent on your deposits.)
- (Round to the nearest cent.)
---
To assist your learning, let's break down the problem into key concepts:
### Key Concepts
- **Future Value (FV) Calculation**: Determine the future value of one or more cash flows given an interest rate and time period.
- **Present Value (PV) Calculation**: Determine the present value of future cash flows discounted at a certain interest rate.
- **Annual Payments (Annuity)**: Calculate the equal payments (annuities) required to reach a future sum of money given an interest rate over a period.
### Graphs or Diagrams
No graphs or diagrams are present in the image.
[Insert your interactive or instructional diagram or graph tool here if needed for the learning activity]
---
**Note**: Make sure to use a financial calculator or spreadsheet software to assist with the exact computations as requested in the problem.
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Transcribed Image Text:## Comprehensive Problem
You would like to have $52,000 in 12 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 10 percent interest compounded annually. Your first payment will be made at the end of the year.
### Questions:
1. **How much must you deposit annually to accumulate this amount?**
- (Round to the nearest cent.)
2. **If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be?**
- (Assume you can earn 10 percent on this deposit.)
- (Round to the nearest cent.)
3. **If you deposit $20,000 received at the end of five years in the bank, what will the amount grow to by the end of year 12?**
- (Round to the nearest cent.)
4. **In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal?**
- (Again, assume you can earn 10 percent on your deposits.)
- (Round to the nearest cent.)
---
To assist your learning, let's break down the problem into key concepts:
### Key Concepts
- **Future Value (FV) Calculation**: Determine the future value of one or more cash flows given an interest rate and time period.
- **Present Value (PV) Calculation**: Determine the present value of future cash flows discounted at a certain interest rate.
- **Annual Payments (Annuity)**: Calculate the equal payments (annuities) required to reach a future sum of money given an interest rate over a period.
### Graphs or Diagrams
No graphs or diagrams are present in the image.
[Insert your interactive or instructional diagram or graph tool here if needed for the learning activity]
---
**Note**: Make sure to use a financial calculator or spreadsheet software to assist with the exact computations as requested in the problem.
Happy Learning!
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