Question

Jill currently has $300,000 in a brokerage account. The account pays a 10 percent annual interest rate. Assuming that Jill makes no additional contributions to the account, how many years will it take for her to have $1,000,000 in the account?

Answer 1

Jill would need approximately 11.53 years for her $300,000 to grow to $1,000,000 at a 10% annual interest rate compounded annually by using the formula for compound interest and solving for the number of years.

Step-by-step explanation:

To determine how many years it will take for Jill's $300,000 to grow to $1,000,000 at an annual interest rate of 10%, compounded annually, we can use the formula for compound interest:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In this case, we are looking for t, so we can rearrange the formula to solve for t:

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

Plugging in the values:

t = ln(1,000,000 / 300,000) / (1 * ln(1 + 0.10 / 1))

t = ln(3.3333) / ln(1.10)

t ≈ 11.53

Therefore, it will take Jill approximately 11.53 years to grow her $300,000 to $1,000,000 with a 10% interest rate compounded annually.

Answer 2

n = 12.63 year

Step-by-step explanation:

Present Value = $300,000

Future Value = $1,000,000

Annual Interest Rate = 10%

Period = n years

Present Value * (1 + Interest Rate)^Period = Future Value

$300,000 * (1 + 0.10)^n = $1,000,000

1.10^n = 3.333

taking log on both side

n * ln(1.10) = ln(3.333)

n = 12.63 year