Question

if $800 are deposited into a savings account with a 3% annual interest rate, compounded annually, what is the account balance after 5 years?
annual compound interest formula
$a = p(1 + r)^t$
$a = \\$?$

Explanation:

Step1: Identify the values

We know that the principal amount \( P = 800 \), the annual interest rate \( r = 3\%=0.03 \), and the time \( t = 5 \) years. The formula for annual compound interest is \( A = P(1 + r)^t \).

Step2: Substitute the values into the formula

Substitute \( P = 800 \), \( r = 0.03 \), and \( t = 5 \) into the formula \( A = P(1 + r)^t \). So we get \( A = 800\times(1 + 0.03)^5 \).

Step3: Calculate \( (1 + 0.03)^5 \)

First, calculate \( 1+ 0.03=1.03 \). Then, \( 1.03^5\approx1.159274 \) (using a calculator to find the fifth power of \( 1.03 \)).

Step4: Calculate the final amount \( A \)

Multiply \( 800 \) by \( 1.159274 \): \( A = 800\times1.159274 = 927.4192 \approx 927.42 \)

Answer:

\( 927.42 \)