Question

if $450 are deposited into an account with a 8.5% interest rate, compounded annually, what is the balance after 9 years? f = $? f = p(1 + \frac{r}{n})^{nt} round to the nearest cent.

Explanation:

Step1: Identify the values

We know that the principal amount \( P = 450 \), the annual interest rate \( r = 8.5\%=0.085 \), the number of times compounded per year \( n = 1 \) (since it's compounded annually), and the number of years \( t = 9 \).

Step2: Substitute into the formula

The compound - interest formula is \( F=P(1 +\frac{r}{n})^{nt} \).
Substitute \( P = 450 \), \( r=0.085 \), \( n = 1 \), and \( t = 9 \) into the formula:
\( F=450\times(1+\frac{0.085}{1})^{1\times9} \)
First, calculate the value inside the parentheses: \( 1+\frac{0.085}{1}=1 + 0.085=1.085 \)
Then, calculate the exponent: \( 1\times9 = 9 \)
So we have \( F = 450\times(1.085)^{9} \)

Step3: Calculate \((1.085)^{9}\)

Using a calculator, \( 1.085^{9}\approx2.07793 \)

Step4: Calculate F

Multiply \( 450 \) by \( 2.07793 \): \( F=450\times2.07793 = 935.0685\approx935.07 \)

Answer:

\( \$935.07 \)