Question

Marvin's goal is to accumulate $1,000,000 in his retirement plan by making contributions of $250

at the end of each month. He expects to earn 10.8% compounded monthly. How long will it take Marv to reach his goal?
(Round up to the nearest whole year)
• 26 years
• 14 years
• 155 years
• 34 years
• 41 years. Which is correct option

Answer 1

Marvin will need approximately 34 years to reach his goal of accumulating $1,000,000 in his retirement plan.

Step-by-step explanation:

To calculate the time it will take for Marvin to reach his goal, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, Marvin's goal is $1,000,000, his monthly contribution is $250, the annual interest rate is 10.8%, and interest is compounded monthly (so n = 12).

Since we want to find t, we can rearrange the formula:

t = log(A/P) / (n * log(1 + r/n))

Plugging in the values, we get:

t = log(1000000/250) / (12 * log(1 + 0.108/12))

t ≈ 33.83 years

Since we need to round up to the nearest whole year, it will take 34 years for Marvin to reach his goal.