Question

Today is Sofia’s 35^th birthday. She plans to retire in 32 years at the age of 67, with expected life expectancy of 30 years after that.

To maintain her life style, she thinks she will have to withdraw $8,000 from retirement account at the beginning of each month during retirement. Meanwhile, she plans to donate $100 to charity starting on her 70^th birthday, and the monthly payment will continue till she passes away. In addition, she would like to establish a scholarship with an annual payment forever, with the first payment of $10,000 to be given out on her 75^th birthday. To keep pace with inflation, Sofia would like the amount of scholarship payments to increase by 2% each year. During retirement, Sofia expects to earn 6% per year compounded semi-annually.

She currently has $40,000 in her investment account that earns 7% interest per year compounded monthly. Separately, Sofia also contributes $100 to her RRSP while her employer contributes $50 every week. These contributions are made at the end of each week until she retires at 67. Sofia expects to earn 8% per year compounded annually on her RRSP contributions prior to retirement.

a) How much money does she need when she retires at the age of 67?

b) How much money will she have when she retires?

c) To deal with any shortfall, Sofia will have to make additional monthly contributions to the retirement account. The contributions will be made at the end of each month until she retires at 67. How much additional amount must she contribute each month to the retirement account?

Answer 1

Expected Life expectancy in years

30

Amount of withdrawal per month

$8,000

Number of months of withrawal

360

(30*12)

Annual interest=6%

Monthly interest=(6/12)=0.5%

A

Amount Required at the age 67 for monthly income for 30 years

$1,341,005

(Using PV function of excel with Rate=0.5%,Nper=360, Pmt=-8000. Type=1)

Value of $100 per month charity at 70th birthday

$            20,000

(100/0.005)

Number of years from her 67th birthday=(70-67)=

3

B

Value of $100 per month charity at 67th birthday

$            16,792

(20000/(1.06^3)

Value of annual payment of $10000 at 75th birthday

$          250,000

(10000/(0.06-0.02)

C

Value of annual payment of $10000 at 67th birthday

$          156,853

(250000/(1.06^8)

75-67=8

D=A+B+C

Total Amount required at the age of 67(Retirement)

$1,514,650

Interest rate before retirement=7%

Monthly interest =(7/12)%

Amount available in account

$40,000

Saving per week

$150

(100+50)

Savings per month =150*(52/12)

$                  650

Number of months savings till retirement

420

(35*12)

Amount accumulated at the time of retirement

$1,630,932

(Using FV function of excel with Rate=(7/12)%,Nper=420, Pmt=-650.PV=40000Type=0)

No additional contribution is required