Erica opened the savings account and deposited $200 as principal the account earns 10% interest compounded annually what is the balance after 6 years use the formula equals p * 1 + r / n to the power of NT where a is the balance p is the principal r is the interest rate represented as a decimal n is the number of times per year that the interest is compounded and t is the time of years round your answer to the nearest cent

Question

GPT-4o mini · Answer

To calculate the balance after 6 years for a savings account with the formula $ A = P \left( 1 + \frac{r}{n} \right)^{nt} $, we will need to identify the values of $ P $, $ r $, $ n $, and $ t $ from your description.

Given:

Principal $ P = 200 $
Interest rate $ r = 10% = 0.10 $
Compounding frequency $ n = 1 $ (since it's compounded annually)
Time $ t = 6 $ years

Now we can substitute the values into the formula:

\[ A = 200 \left( 1 + \frac{0.10}{1} \right)^{1 \cdot 6} \]

Simplifying inside the parentheses:

\[ A = 200 \left( 1 + 0.10 \right)^{6} = 200 \left( 1.10 \right)^{6} \]

Now we need to calculate $ (1.10)^{6} $:

\[ (1.10)^{6} \approx 1.771561 \]

Now substituting back:

\[ A \approx 200 \times 1.771561 \approx 354.3122 \]

Rounding to the nearest cent:

\[ A \approx 354.31 \]

Thus, the balance after 6 years, rounded to the nearest cent, will be $354.31.