Question

1. a. You are currently 25 and plan to retire at age 65. You think you will need $150,000 per year during your retirement years. You assume that you will live until age 90. You also want to leave $1,000,000 to Wingate University when you die at age 90. You expect to get a 6% rate on your investments. How much do you need to have in your account at retirement?

2. If you start saving now at age 25, how much will you need to save each year to meet your goal? If you wait until age 40 to begin saving, how much will you need to save each year? Assume you still earn a 6% rate.

3. Your parents have told you they will give you $50,000 for your 30^th birthday, which you will put into the account. Your employer will match the exact amount each year you put into the account. If you start saving now at age 25, how much will you need to put into the account each year?

Answer 1

Let us assume that that the amount of $150000 is required at the beginning of each year

So, requirement is $150000 at age 65 (day of retirement) every year for 25 years and then $1000000 at the end of 25 years

Balance required in the account at retirement

=150000+150000/1.06+....+150000/1.06^24+1000000/1.06^25

=150000/0.06*(1-1/1.06^25)*1.06+1000000/1.06^25

=$ 2,265,552.26

If first amount of saving (A) is deposited in account today (at age 25) and last installment one year before the retirement, there will be a total of 40 installments

A/0.06*(1.06^40-1)*1.06 = 2265552.26

=> 164.04768*A = 2265552.26

=> A = 13810.33

So, $13810.33 is required every year starting today for 40 years

If first amount of saving (A) is deposited in account at age 40 and last installment one year before the retirement, there will be a total of 25 installments

A/0.06*(1.06^25-1)*1.06 = 2265552.26

=> 58.15638*A = 2265552.26

=> A = 38956.21

So, $38956.21 is required every year starting for 25 years starting age 40

Let X be the amount required each year (including employer's contribution)

30000*1.06^35+X/0.06*(1-1/1.06^40)*1.06 = 2265552.26

=> 164.04768*X = 2034969.66

=> X = 12404.74

So, amount required to be put into account each year = 12404.74/2 = $6202.37

So, $6202.37 is required every year starting today for 40 years