Question

In: Finance

Asma Jaqqa started a job at the government. Her salary is $105,000 before tax and at...

Asma Jaqqa started a job at the government. Her salary is $105,000 before tax and at the end of this year and all subsequent years her salary will increase by 2.5%.

The tax on her income is 30%. Each year-end she deposits 10% of her after tax salary into an RRSP. After 20 years she plans to move to part time, and her pay will drop by 50%.

When she drops to 50% pay, her tax rate will drop to 20%. She will continue to work at this capacity for 10 years until she retires. She will continue to save 10% of her after tax salary each year into an RRSP. She expects she will earn 6% p.a. on the RRSP investments.

REQUIRED:

a) How much will she have in her RRSP after 20 years?







b) How much will she have in her RRSP after 30 years?

c) If the inflation rate is 1.5% p.a. for every year, what is the real value of the 30 year RRSP balance, in today’s dollars?

d) Explain to Asma, using an example from her case, why she should monitor and use this feedback with her financial plan?

Solutions

Expert Solution

a) After tax salary would be $105000*70% =$73500 in the first year and increasing by 2.5% each year till she is full time

Each year she deposits 10% i.e. starting with $7350 at the end of the 1st year and increasing by 2.5% each year

So, Balance in RRSP after 20 years

= 7350*1.06^19+7350*1.025*1.06^18+...........+7350*1.025^19

= 7350*1.06^19*(1-(1.025/1.06)^20)/(1-1.025/1.06)

=329389.00

She will have $329389 in her RRSP account after 20 years

b) Salary at the end of 20 years = $105000*1.025^20 = $172054.73

She gets half the salary after 20 years , Salary in the 21st year = $172054.73 *0.5 =$86027.36

Aftertax salary in 21st year = 86027.36 *0.8 = $68821.89

Her contribution  =10% of $68821.89 = $6882.19

So, balance in RRSP after 30 years

=329389*1.06^10+ (6882.19*1.06^9+6882.19*1.025*1.06^8+.........+6882.19*1.025^9)

=329389*1.06^10 + 6882.19*1.06^9*(1-(1.025/1.06)^10)/(1-1.025/1.06)

=690318.93

She will have $690318.93 in her RRSP account after 30 years

c) Real Value of her RRSP balance in today's dollars = 690318.93/1.015^30 = $441640.12

d) She should monitor this feedback as her retirement will depend not only on the contributions made, but also on the interest amount she is able to earn on her account. The nominal value of wealth is $690318.93 but the real wealth (purchasing power) of that wealth after 30 wealth would only be as good as that of $441640.12 today. So, She should use these inputs in her financial planning.

jeff jeffy answered 1 year ago
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