Question

# You are 23 years old and decide to start saving for your retirement. You plan to...

You are 23 years old and decide to start saving for your retirement. You plan to save \$ 6,500 at the end of each year​ (so the first deposit will be one year from​ now), and will make the last deposit when you retire at age 69. Suppose you earn 12% per year on your retirement savings.

a. How much will you have saved for​ retirement?

b. How much will you have saved if you wait until age 40 to start saving​ (again, with your first deposit at the end of the​ year)?

(a) Annual Year-End Deposits = \$ 6500

Current Age = 23 years and Age of Final Deposit = 69

Deposit Tenure = Number of Deposits = 69 - 23 = 46

Rate of Return = 12 %

Therefore, Total Savings by the age of 69 = 6500 x (1.12)^(45) + 6500 x (1.12)^(44) +......+ 6500 = \$ 9894414.635

(b)

Annual Year-End Deposits = \$ 6500

Age when I start saving = 40 years (actually 41 as that is when I make the first deposit) and Age of Final Deposit = 69

Deposit Tenure = Number of Deposits = 69 - 40 = 29

Rate of Return = 12 %

Therefore, Total Savings by the age of 69 = 6500 x (1.12)^(28) + 6500 x (1.12)^(27) +......+ 6500 = \$ 1394787.9