How much do you need to deposit to withdraw $9,000 a year for 8 years?

  

How much do you have to deposit today so that beginning 11 years from now, you can withdraw $9,000 a year for the next eight years (periods 11 through 18) plus an additional amount of $18,000 in the last year (period 18)? Assume an interest rate of 8%. What is the amount of money you would need to deposit today?

Introduction:
When planning for our financial future, it is essential to know how much we need to save or invest to achieve our financial goals. One of those goals could be to have a steady income over a specific period. In this scenario, we will look at how much you would have to deposit today to withdraw a fixed amount annually and a lump sum amount at the end.

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Description:
If you plan to withdraw $9,000 every year for eight years starting from year 11 and get an additional amount of $18,000 at the end of year 18, your first step is to calculate how much you would need to deposit currently. Assuming an annual interest rate of 8% for the entire period, the amount of money you would need to deposit today is the present value of the future cash flows. To calculate this, you would need to use the present value formula, which takes into account the future cash flows and the interest rate. Once you have calculated the present value, you will know how much you need to deposit today to achieve your financial goal.

Heading: Financial Planning

Objective:
To determine the amount of money to be deposited today in order to withdraw a fixed amount annually for eight years with a lump sum amount to be withdrawn at the end of the period, by using the given interest rate of 8%.

Learning outcomes:
– Understand the concept of time value of money
– Learn to use the present value formula to calculate the current value of future payments
– Understand how to use the interest rate to discount future cash flows
– Calculate the amount of money that needs to be deposited today to meet a future financial goal.

Heading: Investments

Objective:
To calculate the present value of future cash flows and determine whether the investment is feasible or not, by considering the given interest rate of 8%.

Learning outcomes:
– Use the present value formula to calculate the current value of future payments, based on the given interest rate.
– Understand the relationship between the present value of future cash flows and the interest rate
– Evaluate the feasibility of an investment based on the amount of money that needs to be invested today to reach a financial goal.

Heading: Time Value of Money

Objective:
To illustrate the concept of the time value of money and how it relates to investment planning, by calculating the present value of future cash flows using the given interest rate of 8%.

Learning outcomes:
– Understand the concept of time value of money and how it influences investment planning
– Calculate the present value of future payments
– Understand how the present value of future cash flows is related to the interest rate
– Explain how changes in interest rates impact investment decisions.

Solution 1: Calculate Present Value using Annuity Formula

To calculate the present value of the future cash flows, we can use the annuity formula. We know that the cash flows are $9,000 for 8 years and an additional $18,000 in the 8th year. The interest rate is 8%.

PV = C * [(1 – (1 / (1 + r)^n)) / r] + FV / (1 + r)^n

Where:
C = Cash flow per period
r = Interest rate
n = Number of periods
FV = Future value

Using this formula, we can calculate the present value of the cash flow as follows:

PV = $9,000 * [(1 – (1 / (1 + 0.08)^8)) / 0.08] + $18,000 / (1 + 0.08)^8
PV = $54,570.76

Therefore, you would need to deposit $54,570.76 today to be able to withdraw $9,000 a year for the next 8 years and an additional $18,000 in the last year, beginning 11 years from now.

Solution 2: Calculate Present Value using Present Value of a Lump Sum Formula

Alternatively, we can calculate the present value of the future cash flows using the present value of a lump sum formula. The formula is:

PV = FV / (1 + r)^n

Where:
FV = Future value
r = Interest rate
n = Number of periods

Using this formula, we can calculate the present value of the cash flow as follows:

PV = ($9,000 * ((1 – (1 / (1 + 0.08)^8)) / 0.08)) * (1/(1 + 0.08)^11) + $18,000 / (1 + 0.08)^18
PV = $54,570.76

Therefore, you would need to deposit $54,570.76 today to be able to withdraw $9,000 a year for the next 8 years and an additional $18,000 in the last year, beginning 11 years from now.

Suggested Resources/Books:

1. “Fundamentals of Financial Management” by Eugene F. Brigham and Joel F. Houston
2. “Corporate Finance” by Jonathan Berk and Peter DeMarzo
3. “Financial Markets and Institutions” by Frederic S. Mishkin and Stanley G. Eakins
4. “The Intelligent Investor” by Benjamin Graham
5. “Investments” by Zvi Bodie, Alex Kane, and Alan J. Marcus

Similar Asked Questions:

1. What is the present value of a future cash flow?
2. What is the future value of a present amount of money?
3. How do interest rates affect the present value of future cash flows?
4. What is an annuity and how does it work?
5. How much money do I need to save today to achieve a specific future goal?

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