When Steve and Roslyn retire together they wish to receive $40,000 additional income (in the equivalent of today’s dollars) at the beginning of each year. They assume inflation will be 4% and they expect to realize an after tax return of 8%. Based on life expectancies, they estimate their retirement period to be about 30 years. They want to know how much they will need to have in their fund at the time of their retirement.

Question

When Steve and Roslyn retire together they wish to receive $40,000 additional income (in the equivalent of today’s dollars) at the beginning of each year. They assume inflation will be 4% and they expect to realize an after tax return of 8%. Based on life expectancies, they estimate their retirement period to be about 30 years. They want to know how much they will need to have in their fund at the time of their retirement.

I think on the financial calculator
solving for PV.Not sure what Interest is if this correct?
N=30
PMT=40,000
I=?
Pv
FV=0

Answer 1

To calculate the present value (PV) of the retirement fund that Steve and Roslyn will need, we can use a financial calculator or a financial formula.

Here's how you can calculate it using a financial calculator:

1. Set the number of periods (N) to 30, as they expect their retirement period to be around 30 years.
2. Set the payment per period (PMT) to -$40,000. It is negative because it represents an outgoing cash flow.
3. Set the future value (FV) to 0, as they want to have consumed all their funds by the end of their retirement period.
4. Set the interest rate (I) to find the present value (PV).

Now, to solve for I(interest), you will need to input the other values into your financial calculator. However, in your question, the interest rate is not provided, only the expected after-tax return rate of 8%.

Typically, when calculating retirement funds, the interest rate used is the rate of return on their investments. However, in this case, although we have the after-tax return of 8%, we don't know the tax rate applied to the returns.

To proceed with the calculation, you would need the specific interest rate to accurately calculate the present value (PV) of their retirement fund. Once you have the interest rate, input the values into your financial calculator to solve for PV.

Note: Keep in mind that the assumptions made in this calculation may not reflect the actual financial situation of Steve and Roslyn. It is always recommended to consult with a financial advisor or planner for personalized advice.

Answer 2

To calculate the present value (PV) of the retirement fund needed, we can use the formula for the present value of an annuity.

PV = PMT * ((1 - (1 + I)^(-N)) / I)

Where:
PV is the present value
PMT is the yearly payment they wish to receive at the beginning of each year ($40,000)
I is the interest rate (after tax return rate of 8%)
N is the number of years (30)

Let's calculate the present value using the provided information.

PV = $40,000 * ((1 - (1 + 0.08)^(-30)) / 0.08)

Simplifying the equation,

PV = $40,000 * ((1 - 1.08^(-30)) / 0.08)

PV = $40,000 * (1 - 0.188686) / 0.08

PV = $40,000 * 0.811314 / 0.08

PV ≈ $405,657.69

Therefore, Steve and Roslyn will need approximately $405,657.69 in their retirement fund at the time of retirement to receive $40,000 additional income (in today's dollars) at the beginning of each year.