Question

use the formula $a = p(1 + \frac{r}{n})^{nt}$ to find the total amount in an account after 6 years if the initial deposit is $300.00 and it is compounded annually at 6%. round to the nearest cent.

Explanation:

Step1: Identify variables

Given: \( P = 300 \), \( r = 0.06 \) (6% as decimal), \( n = 1 \) (compounded annually), \( t = 6 \).

Step2: Substitute into formula

Substitute values into \( A = P(1 + \frac{r}{n})^{nt} \):
\( A = 300(1 + \frac{0.06}{1})^{1 \times 6} \)

Step3: Simplify exponent and base

Simplify: \( 1 + 0.06 = 1.06 \), \( 1 \times 6 = 6 \). So \( A = 300(1.06)^6 \)

Step4: Calculate \( (1.06)^6 \)

\( (1.06)^6 \approx 1.418519112 \)

Step5: Multiply by P

\( A = 300 \times 1.418519112 \approx 425.5557336 \)

Step6: Round to nearest cent

Round to two decimal places: \( \$425.56 \)

Answer:

\$425.56