Questions: Find the compound amount on a deposit of 7610 at 9% for 8 years by multiplying the original amount deposited by 100% plus the compound rate. The compound amount is . (Round to the nearest hundredth.)

Solution Steps

To find the compound amount, we use the formula for compound interest: \( A = P(1 + r)^n \), where \( A \) is the amount of money accumulated after n years, including interest. \( P \) is the principal amount (initial deposit), \( r \) is the annual interest rate (as a decimal), and \( n \) is the number of years the money is invested for. We will plug in the given values into this formula to calculate the compound amount.

We are given the following values:

• Principal amount \( P = 7610 \)
• Annual interest rate \( r = 0.09 \)
• Number of years \( n = 8 \)

We use the compound interest formula: \[ A = P(1 + r)^n \] Substituting the known values: \[ A = 7610(1 + 0.09)^8 \]

Calculating \( (1 + 0.09)^8 \): \[ (1 + 0.09)^8 \approx 1.85093 \] Now, substituting this back into the equation: \[ A \approx 7610 \times 1.85093 \approx 14066.4 \]

Rounding the compound amount to the nearest hundredth gives: \[ A \approx 15163.40 \]

Final Answer