Question

simon has $6,290 in an account. the interest rate is $9\frac{83}{100}\\%$ compounded annually. to the nearest cent, how much will he have in 2 years? $

Explanation:

Step1: Convert the mixed fraction interest rate to decimal

The interest rate is \( 9\frac{83}{100}\% \), which is \( 9.83\% \). To convert this to a decimal, we divide by 100, so \( r = 0.0983 \).

Step2: Recall the compound - interest formula

The formula for compound interest is \( A=P(1 + r)^t \), where:

• \( P \) is the principal amount (the initial amount of money). Here, \( P=\$6290 \).
• \( r \) is the annual interest rate (in decimal form). We found \( r = 0.0983 \).
• \( t \) is the number of years. Here, \( t = 2 \).

Step3: Substitute the values into the formula

Substitute \( P = 6290 \), \( r=0.0983 \), and \( t = 2 \) into the formula \( A = P(1 + r)^t \):
\( A=6290\times(1 + 0.0983)^2 \)
First, calculate \( 1+0.0983=1.0983 \).
Then, calculate \( 1.0983^2=1.0983\times1.0983 = 1.20626289 \).
Next, multiply this by 6290:
\( A=6290\times1.20626289 \)
\( A = 6290\times1.20626289=7587.4035781 \)

Answer:

\( \$7587.40 \) (rounded to the nearest cent)