Jeanette wishes to retire in 30 years at age 55 with retirement savings that have the purchasing power of $300,000 in today’s dollars.

1. If the rate of inflation for the next 30 years is 2% per year, how much must she accumulate in her RRSP?

2. If she contributes $3000 at the end of each year for the next five years, how much must she contribute annually for the subsequent 25 years to reach her goal? Assume that her RRSP will earn 8% compounded interest annually.

3. The amount in Part (a) will be used to purchase a 30-year annuity. What will the month-end payments be if the funds earn 6% compounded interest monthly?

1. At a rate of inflation of 2%, the value of today's 300,00 in 30 years is

300,000(1.02)^30 = $ 543,408.48

2.

(3000(1.08^5 - 1)/.08) (1.08)^25 + x(1.08^25 - 1)/.08 = 543408.48

I will leave all that button-pushing up to you to solve for x

3.

x( 1 - 1.005^-360)/.005 = 543408.48
x = 3258.01 per month

To answer the questions, we need to use some financial formulas. Here's a step-by-step explanation of how to solve each question:

1. To calculate the amount Jeanette needs to accumulate in her RRSP, we have to adjust the desired retirement savings of $300,000 for inflation. The formula to account for inflation is:

Adjusted value = Present value / (1 + inflation rate)^number of years

In this case, the inflation rate is 2% per year and the number of years is 30. So, plug in the values into the formula:

Adjusted value = $300,000 / (1 + 0.02)^30
Adjusted value ≈ $548,018.73

Therefore, Jeanette must accumulate approximately $548,018.73 in her RRSP to account for inflation.

2. To determine the annual contributions Jeanette needs to make to reach her retirement goal, we can use the future value of an ordinary annuity formula:

Future value = P * [(1 + r)^n - 1] / r

In this case, the annual contribution amount is $3000, the interest rate is 8% compounded annually, and the duration is 25 years (subsequent to the initial 5 years). Rearrange the formula to solve for P:

P = Future value * [r / (1 + r)^n - 1]

Plug in the values into the formula:

P = $548,018.73 * [0.08 / (1 + 0.08)^25 - 1]
P ≈ $2,671.20

Therefore, Jeanette needs to contribute approximately $2,671.20 annually for the subsequent 25 years to reach her goal.

3. To calculate the monthly-end payments for a 30-year annuity, we can use the present value of an ordinary annuity formula:

Present value = P * [1 - (1 + r)^(-n)] / r

In this case, the present value is the accumulated amount in the RRSP of $548,018.73, the interest rate is 6% compounded monthly, and the duration is 30 years. Rearrange the formula to solve for P:

P = Present value * [r / (1 - (1 + r)^(-n))]

Plug in the values into the formula:

P = $548,018.73 * [0.06 / (1 - (1 + 0.06)^(-30))]
P ≈ $3,060.65

Therefore, the month-end payments for the annuity would be approximately $3,060.65.

Please note that these calculations are approximations and do not take into account taxes or other factors specific to Jeanette's situation. It's always recommended to consult a financial advisor for personalized advice.