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Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest. You deposit \( \$ 3500 \) in an account with an annual interest of \( 5.7 \% \) for 10 years. The amount of money you'll have at the end of 10 years is \$ \( \square \) (Type an integer or a decimal.)

Ask by Murray Romero. in the United States
Feb 22,2025

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Answer

The amount of money you'll have at the end of 10 years is \$5,495.

Solution

To find the final amount with simple interest, use the formula:   A = P × (1 + r × t) where  P = initial deposit = 3500,  r = annual interest rate in decimal = 5.7% = 0.057,  t = time in years = 10. Plug in the numbers:   A = 3500 × (1 + 0.057 × 10)   A = 3500 × (1 + 0.57)   A = 3500 × 1.57   A = 5495 Thus, the amount of money you'll have at the end of 10 years is $5495.

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To calculate the total amount of money at the end of 10 years with simple interest, you can use the formula: \[ A = P + (P \times r \times t) \] Where: - \( A \) is the total amount of money after the interest. - \( P \) is the principal amount (initial deposit) – in this case, \( \$ 3500 \). - \( r \) is the annual interest rate (as a decimal) – \( 5.7\% = 0.057 \). - \( t \) is the time in years – \( 10 \) years. Calculating each part: 1. Calculate the interest earned: \[ Interest = P \times r \times t = 3500 \times 0.057 \times 10 = 1995 \] 2. Now add this interest to the principal: \[ A = 3500 + 1995 = 5495 \] So, the total amount of money you'll have at the end of 10 years is \( \$ 5495 \).

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