Today is your 21^st birthday and you just decided to start saving money so you can retire early. Thus, you are going to save $500 a month starting one month from now. You plan to retire as soon as you can accumulate $1 million. If you can earn an average of 8 percent on your savings, how old will you be when you retire?

Question

Quizplus · Accepted Answer

To find out how many years it will take to accumulate $1 million, we can use the formula for future value of an annuity:

FV = Pmt x (((1 + r)^n - 1) / r)

where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.

Plugging in the numbers, we get:

$1,000,000 = $500 x (((1 + 0.08/12)^n - 1) / (0.08/12))

Simplifying this equation, we get:

2,000 = ((1 + 0.08/12)^n - 1)

Using a calculator or spreadsheet, we can solve for n, which is the number of months it will take to accumulate $1 million:

n = 505.93 months

Dividing this by 12 gives us the number of years:

n = 42.16 years

Since we are starting one month from now, we need to add one more month, which gives us:

n = 42.17 years

Therefore, we will retire when we are approximately 54.39 years old (21 + 42.17). The answer is C.

Today Is Your 21st Birthday and You Just Decided to Start

Today Is Your 21^st Birthday and You Just Decided to Start