Question

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?

Answer 1

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

Answer 2

3.

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