Today,you turn 21. Your birthday wish is that you will be a millionaire by your 40^th birthday. In an attempt to reach this goal,you decide to save $25 a day,every day until you turn 40. You open an investment account and deposit your first $25 today. What rate of return must you earn to achieve your goal?

Question

Quizplus · Accepted Answer

To become a millionaire by the time of the 40th birthday, the person has 19 years to save, since they start at age 21 and need to have the money by age 40.

The person will save $25 every day for 365 days for 19 years, which equals:

$25 x 365 days x 19 years = $172,625

To determine the interest rate needed to turn $172,625 into $1,000,000, the formula for future value must be used:

FV = PV x (1 + r) ^ n

Where:

FV = Future Value 
PV = Present Value ($172,625) 
r = Interest rate 
n = Number of compounding periods (in this case, 19)

Rearranging the formula to solve for r:

r = (FV / PV) ^ (1/n) - 1

r = ($1,000,000 / $172,625) ^ (1/19) - 1

r = 15.07%

Therefore, the person must earn a rate of return of 15.07% to achieve their goal of becoming a millionaire by the age of 40 by saving $25 a day.

Today,you Turn 21