Question

Neil deposited $8,000.00 into a new savings account that earns 15% interest compounded annually. How long will it take for the balance to grow to $29,885.00?

Answer 1

7.5 years

Explanation:

To determine how long it will take for the balance to grow to $29,885.00 with an interest rate of 15% compounded annually, we can use the formula for compound interest:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

Where:

-
`\( A \)` is the final amount (the desired balance of $29,885.00).

-
`\( P \)` is the initial principal (the initial deposit of $8,000.00).

-
`\( r \) is the annual interest rate of (15 percent or 0.15`

-
`\( n \)` is the number of times the interest is compounded per year (annually, so
`\( n = 1 \)).`

-
`\( t \)` is the number of years.

We need to solve for
`\( t \)`. Plugging in the given values:

`\[ 29885 = 8000 * \left(1 + (0.15)/(1)\right)^(1 * t) \]`

Now, we'll solve for
`\( t \)`:

`\[ \left(1.15\right)^t = (29885)/(8000) \]\\\[ t = \log_(1.15) \left((29885)/(8000)\right) \]`

Using a calculator, you can find that
`\( t \approx 7.5 \)`

So, it will take approximately 7.5 years for the balance to grow to $29,885.00 with an interest rate of 15% compounded annually.