You are a financial planner and have a client who would like to receive a $12,000 annuity for 25 years after retiring 20 years from now. Assuming an 8% return on investment can be earned prior to retirement and a 10% return can be earned after retirement, how much would you advise your client to invest annually, over the next 20 years, to achieve her retirement goal? Please don't use a financial calculator and show all work by doing step by step procedures showing all figures of getting there! thanks so much!!

Question

You are a financial planner and have a client who would like to receive a $12,000 annuity for 25 years after retiring 20 years from now. Assuming an 8% return on investment can be earned prior to retirement and a 10% return can be earned after retirement, how much would you advise your client to invest annually, over the next 20 years, to achieve her retirement goal? Please don't use a financial calculator and show all work by doing step by step procedures showing all figures of getting there! thanks so much!!

Answer 1

To calculate the annual investment needed to achieve the retirement goal, we need to break down the problem into two parts:

Part 1: Accumulate the Future Value of Investment Prior to Retirement:
1. Determine the number of years till retirement: 20 years.
2. Calculate the future value of investment prior to retirement using the formula:
Future Value = Present Value * (1 + Interest Rate)^Number of Years.

Given:
- Present Value = Annual Investment (to be determined),
- Future Value = ? (unknown),
- Interest Rate = 8%.
- Number of Years = 20.

We can rewrite the formula as:
Future Value = Annual Investment * (1 + 0.08)^20.

Part 2: Accumulate the Annuity for 25 years after Retirement:
1. Determine the number of years for the annuity: 25 years.
2. Calculate the present value of the annuity using the formula:
Present Value = Annual Annuity Payment * (1 - (1 + Interest Rate)^(-Number of Years)) / Interest Rate.

Given:
- Annual Annuity Payment = $12,000,
- Present Value = ? (unknown),
- Interest Rate = 10%,
- Number of Years = 25.

We can rewrite the formula as:
$12,000 = Present Value * (1 - (1 + 0.10)^(-25)) / 0.10.

Now, let's solve each part step by step:

Part 1: Accumulate the Future Value of Investment Prior to Retirement:
Using the formula mentioned earlier:
Future Value = Annual Investment * (1 + 0.08)^20.

We want to solve for Annual Investment:
Future Value = Annual Investment * (1.08)^20.

Rearranging the formula:
Annual Investment = Future Value / (1.08)^20.

Part 2: Accumulate the Annuity for 25 years After Retirement:
Using the formula for Present Value of an Annuity:
$12,000 = Present Value * (1 - (1 + 0.10)^(-25)) / 0.10.

Rearranging the formula:
Present Value = $12,000 * 0.10 / (1 - (1.10)^(-25)).

Finally, let's calculate the values:

Part 1:
Future Value = $12,000 * (1.08)^20.
≈ $45,259.26.

Annual Investment = $45,259.26 / (1.08)^20.
≈ $9,479.40.

Part 2:
Present Value = $12,000 * 0.10 / (1 - (1.10)^(-25)).
≈ $101,484.34.

Therefore, you would advise your client to invest approximately $9,479.40 annually for the next 20 years to achieve her retirement goal of receiving a $12,000 annuity for 25 years after retiring 20 years from now.