Today is your 25th birthday. Your goal is to have $2 million by the time you ret
ID: 2755998 • Letter: T
Question
Today is your 25th birthday. Your goal is to have $2 million by the time you retire at age 65. So far you have nothing saved, but you plan on making the first contribution to your retirement account today. You plan on making three other contributions to the account, one at age 30, age 35, and age 40. Since you expect that your income will increase rapidly over the next several years, the amount that you contribute at age 30 will be double what you contribute today, the amount at age 35 will be three times what you contribute today, and the amount at age 40 will be four times what you contribute today. Assume that your investments will produce an average annual return of 10%. Given your goal and plan, what is the minimum amount you need to contribute to your account today?
Explanation / Answer
Let un assume a contribution of X $ at the age of 25 At the age of 30, the contribution will be 2X $ At the age of 35, the contribution will be 3X $ At the age of 40, the contribution will be 4X $ Average Rate of Return = 10% Amount to be saved at the age of 65 years = $ 2 million (40 years from now) Thus, the interest on First Contribution X * 10% * 40 Second Contribution 2X * 10% * 35 Third Contribution 3X * 10% * 30 Fourth Contribution 4X * 10% * 25 Combining all these elements, X + 2X + 3X + 4X + 4X + 7X + 9X + 10X = 2,000,000 Therefore, working out the equation, X = 50000 $ Thus, the minimum amount needed to be contributed today is $ 50,000.