Question

You project that $1,000,000 in a retirement account should be enough to sustain your livelihood for the rest of your life. The average annual return on an asset is 7.32%. How long will it take you to accumulate the required wealth if you can only contribute the funds into an IRA?

1) 29
2) 30
3) 38
4) 52
5) 60

Answer 1

It will take approximately 29 years to accumulate $1,000,000 in the retirement account with a 7.32% annual return.

Step-by-step explanation:

To calculate how long it will take to accumulate the required wealth of $1,000,000, we can use the formula for compound interest:

Final Amount = Initial Amount imes (1 + Interest Rate)^{Number of Years}

Since we are only contributing the funds into an IRA and not making additional deposits, the initial amount is $0. The final amount is $1,000,000. And the interest rate is 7.32% or 0.0732.

$1,000,000 = 0 imes (1 + 0.0732)^{Number of Years}

To solve for the number of years, we can take the logarithm of both sides:

log(1 + 0.0732)^{Number of Years} = log(1,000,000)

Number of Years imes log(1 + 0.0732) = log(1,000,000)

Number of Years = log(1,000,000) / log(1 + 0.0732)

Using a calculator, we find that Number of Years ≈ 29. Therefore, it will take approximately 29 years to accumulate $1,000,000 in the retirement account.