Question

ivy is saving money to buy some corazs. she invests $210 in a savings account that earns $9\frac{1}{2}\\%$ interest, compounded annually. how much money will she have in her account after 6 years? answer in dollars and round to the nearest cent.

Explanation:

Step1: Convert rate to decimal

First, convert $9\frac{1}{2}\%$ to a decimal. $9\frac{1}{2} = 9.5$, so $9.5\% = \frac{9.5}{100} = 0.095$.

Step2: Use compound interest formula

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

• $P = 210$ (principal amount),
• $r = 0.095$ (annual interest rate),
• $t = 6$ (number of years).

Substitute values:
$A = 210(1 + 0.095)^6$

Step3: Calculate $(1.095)^6$

First compute $1.095^6 \approx 1.72379$

Step4: Multiply by principal

$A = 210 \times 1.72379 \approx 362.00$

Answer:

$362.00$