Martina puts \( \$ 8,316.00 \) into an account to use for school expenses. The account earns \( 13.7 \% \) interest, compounded monthly. How much will be in the account after 7 years? Use the formula \( A=P\left(1+\frac{r}{n}\right)^{\text {nt }} \), where \( A \) is the balance (final amount), \( P \) is the principal (starting amount), \( r \) is the interest rate expressed as a decimal, \( n \) is the number of times per year that the interest is compounded, and \( t \) is the time in years. Round your answer to the nearest cent.

Let's break it down using the formula provided: \( A = P\left(1+\frac{r}{n}\right)^{nt} \) Here, we have: - \( P = 8316 \) - \( r = 0.137 \) (which is \( 13.7\% \) as a decimal) - \( n = 12 \) (since interest is compounded monthly) - \( t = 7 \) Plugging in the numbers: \[ A = 8316 \left(1 + \frac{0.137}{12}\right)^{12 \times 7} \] Calculating \( \frac{0.137}{12} \): \[ \frac{0.137}{12} \approx 0.0114167 \] Now, calculate inside the parentheses: \[ 1 + 0.0114167 \approx 1.0114167 \] Now, raise this to the power of \( 12 \times 7 = 84 \): \[ A \approx 8316 \times (1.0114167)^{84} \] Calculating \( (1.0114167)^{84} \approx 2.64368507 \): \[ A \approx 8316 \times 2.64368507 \approx 21961.11 \] Thus, after rounding to the nearest cent, the final amount in the account after 7 years will be **$21,961.11**. Now let's add some extra flair to this calculation. Thinking of future plans? You just learned that your $8,316.00 investment will grow to $21,961.11 after 7 years, thanks to that sweet 13.7% interest. That’s not just numbers; it’s a ticket to your academic journey or maybe even a trendy gadget for your studies! And remember, the magic of compounding interest means the longer you let your money sit, the more it grows! So think about putting your savings to work early on!