Question

It is your 25^th birthday (end of 25 years) and you decide that you want to retire on your 65^th birthday (end of 65 years - 40 years later). Your salary is $55,000 per year and you expect your salary to increase by 3% each year for the next 40 years. When you retire, you want your retirement fund to provide an annual payment equal to 80% of your salary at age 65 and to increase by 2% a year (to cover inflation) through the end of your retirement. You estimate your retirement will last 25 years (age 65-89 - 25 payments). You want to leave your children the sum of $750,000 when you die on your 90^th birthday. You do not want to work during your retirement and you are not counting on Social Security to provide anything during your retirement. Since you don't want to work during your retirement, you need to have all your money in the retirement fund on the day you retire (65 years old) and you also make the first retirement payment to yourself on your 65^th birthday. All calculations take place at the end of each year therefore you can use the rate tables.

Your expected rate of return (investment rate) for the entire period of time (65 years) is 5%. You are determined to save $15,000 a year for the first 20 years and $25,000 a year for the remaining 20 years until you retire.

1.      What will your salary be at age 65 (40 years from today)? How much is 80% of that salary (retirement goal) and how much income per year does your retirement fund need to provide if your needs increase by 2% a year?

2.      How much will you need in your retirement fund on the day you retire in order to receive the amounts in question #1 and leave the inheritance to your children? Show proof for the 26 payments (including inheritance) that you have enough in the fund?

3.      How much will you have saved (retirement fund) on the day you retire?

4.      If the answers to Questions #2 and #3 are different, how much are you either over or short in your retirement fund?

5.      If you are over or short in your account, how much should you have saved per year in order to have enough in your retirement fund? The assumption for this part of the problem is that you saved an equal amount per year (annuity) for the 40 years; not the $15,000 for the first 20 years and $25,000 for the remaining 20 years.

6.      If you were short in what you needed in the fund, how much could the actual retirement fund that you have in place provide you assuming you wanted an equal amount each year (annuity) and you still want to leave your children the $750,000 inheritance?

7.      You are too depressed by how much you have to save per year over the next 40 years so you decide to continue to have a good time and spend your money, and you don't start saving until you are 35 years old. For the next 30 years, you save $35,000 a year. How much will be in the fund on the day that you retire? How much will you have to save per year to have enough in your retirement fund on your 65^th birthday? All assumptions are the same (inflation and investment) as before.

8.      How much have you saved (invested) into the fund (excluding interest) if you start saving at 25 years old and how much have you saved (invested) into the fund (excluding interest) if you wait and start saving at 35 years old? How much more will you have in your retirement fund starting at 25 versus 35?

Answer 1

Answer:

1 (A)

Salary after 40 years i.e 65 years of age=

$55000(1+0.03)^40

=55000*3.622038

=179412.1

1 (B)

80% of Salary= 179412.1*.8

=143529.7

1(C)

Per year income to be provided by retirement fund=

Total amount needed=143529.7

Let per year income be X

X*(1.02)^40

2.20804X=143529.7

X=65003.21