James and Joanna Buckle are 40 years old and want to retire at age 60. Joanna works for the Federal government, which allows her to retire with a pension that will pay her $40,000 per year, indexed for inflation, provided she completes 30 years of service. Joanna has been working for the government for 10 years and has 20 more years to go. She currently gets paid $80,000 a year and her salary increases each year with inflation.

James is a photographer. He owned a company which lost money and went bankrupt. However, James managed to find a job that pays $65,000 a year. James has saved $20,000 in an RRSP for his retirement and he believes now is the time to plan for retirement.

If James and Joanna Buckle both retire at age 60, they would have to live off Joanna’s defined benefit pension and James RRSP savings, for the first 5 years. At age 65, they would begin receiving government benefits. They estimate that for both of them they would receive $12,000 p.a. before tax. Joanna does not have RRSP contribution room, but James does. So, their retirement savings plan is to contribute $10,000 per year, in real dollars, into James’s RRSP.

Based on their lifestyle, they estimate that they need $65,000 p.a. in after-tax income, in retirement, for 30 years. Their average tax rate in retirement will be 20%.

In addition, when they retire, they want to buy an art studio. Today the art studio costs $125,000, but this will increase with inflation. They currently have $30,000 saved in a TFSA. They will use any tax refunds from James RRSP contributions to save for the studio. James’ current average tax rate is 25% and his marginal tax rate is 30%.

Assumptions. Their investments will earn 8% return before tax. Inflation is 3% p.a. Use only ordinary annuities in this question (not annuities due). Round to the nearest dollar and show your work.

Required

a.            What is James and Joanna’s real rate of return as a percentage rounded to 2 decimals places? 

b.            How much do they need to have saved at age 60 to fund their retirement income in real before tax dollars (excluding the art studio)? Draw a timeline. 

c.             Will they have saved enough in their RRSP at age 60 to fund their retirement income (excluding the art studio)? 

d.            How much will they have to purchase the art studio in real dollars?

Answer rating: 100% (QA)

A The real rate of return formula is the sum of one plus the nominal rate divided by the sum of one plus the inflation rate which then is subtracted by one The formula for the real rate of return can ... View the full answer