Question

Sofia is 45 years old. She has 3 children, Meg age 12, Jo age 14 and Amy age 15. However, she is already planning for retirement. She plans on retiring in 15 years when she will be 60 years old. Sofia believes she will live until she is 100.

In order to live comfortably, she thinks she will need to withdraw $12,000 every month during retirement. These weekly withdrawals will be made at the beginning of each month during retirement. Being a lover of animals, Sofia has pledged to donate $1,000 a week to “World Wide Fund for Nature” during her retirement. The payments will be made at the end of each week. The last payment will be made when she dies. In addition, she would like to establish a scholarship at Ryerson. The first payment from scholarship would be $90,000. The first scholarship payment would be made 6 years after she retires. Thereafter scholarship payments will be made every year. In order to keep pace with inflation, Sofia would like the amount of scholarship payments to increase by 3% each year. She wants the payments to continue after her death, therefore the payments will go on forever. During retirement, Sofia expects to earn 4% per year compounded semi-annually. Sofia also wishes to give each of children $150,000 when they reach the age of 35.

She currently has $120,000 in a locked-in investment that earns 5% interest per year compounded monthly. Sofia currently contributes $200 every week to an investment account. These contributions are made at the end of each week and will continue until she retires at 60. Sofia expects to earn 6% per year compounded annually on her weekly contributions to her retirement account.

1. How much money does she need when she retires at the age of 60? Be certain to include all her financial goals.

2. How much money will she have when she retires?

3. How much is she short? [Hint: that would be the difference between the amounts in parts (a) and (b)]

4. In order to finance any shortfall, Sofia will make weekly contributions into a new retirement account. This new retirement account will earn 8% per year compounded semi-annually. The contributions will be made at the end of each week until she retires at 60. How much must she contribute each week to the new retirement account?

Answer 1

a.Money that she need at the time of 60 years to include her all financial goals :

Statement showing the money needed at the age of 60 years( one year calculation)

PARTICULARS	AMOUNT
Monthly withdrawal (12000*12)	1,44,000
Donation weekly( 1000*52)	52,000
weekly contribution (200*52)	10,400
The total amount that she have need at the age of 60 is ;	2,06,400

note:

1. This statement shows the amount of money required by Sofia to meet her financial goals .
2. Number of weeks in a year is 52.
3. Scholarship of $ 90,000 is paid after yhe retirement of 6 years ,so it is not take .
4. Contribution to an investment is made at the end of the week .
5. At the age of 60 , her children doesn't attain the age 35 years ,so this can be excluded from the calculation .

b) The money she have  at the time of retirement :

Statement showing money that she have

PARTICULARS	AMOUNT
Interest on investment @ the rate of 5%p.a	1,26,000
Interest on weekly contribution @ the rate of 6%p.a	11,024
The total that she have at the time of retirement is	1,37,024

notes:

1. In the question , there is is expected interest rate of 4% p.a compounded semi-annually , since the principal amount is not given .

c) The shortfall in the amount is $ 2,06,400 - $ 1 ,37,024 = $ 69,376.

d) 8% per year compounded semi - annually is $ 22,464.These much is contribute each week .