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Martin has $3,582 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will he have in 1 year?
Use the formula B=p(1+r)^(t), where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
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Martin has $3,582 \$ 3,582 in an account that earns 5% 5 \% interest compounded annually.\newlineTo the nearest cent, how much will he have in 11 year?\newlineUse the formula B=p(1+r)t B=p(1+r)^{t} , where B B is the balance (final amount), p p is the principal (starting amount), r r is the interest rate expressed as a decimal, and t t is the time in years.\newline$ \$ \square

Full solution

Q. Martin has $3,582 \$ 3,582 in an account that earns 5% 5 \% interest compounded annually.\newlineTo the nearest cent, how much will he have in 11 year?\newlineUse the formula B=p(1+r)t B=p(1+r)^{t} , where B B is the balance (final amount), p p is the principal (starting amount), r r is the interest rate expressed as a decimal, and t t is the time in years.\newline$ \$ \square
  1. Identify Given Values: Identify the given values from the problem.\newlinePrincipal pp = $3,582\$3,582\newlineInterest rate rr = 5%5\% or 0.050.05 when expressed as a decimal\newlineTime tt = 11 year\newlineWe will use the compound interest formula B=p(1+r)tB = p(1 + r)^t to find the balance after 11 year.
  2. Substitute Values: Substitute the given values into the compound interest formula.\newlineB=($3,582)(1+0.05)1B = (\$3,582)(1 + 0.05)^1
  3. Calculate Inside Parentheses: Calculate the value inside the parentheses.\newline1+0.05=1.051 + 0.05 = 1.05
  4. Raise to Power: Raise 1.051.05 to the power of 11, which is simply 1.051.05 since any number to the power of 11 is the number itself.\newline1.051=1.051.05^1 = 1.05
  5. Multiply Principal: Multiply the principal by the result from Step 44 to find the balance after 11 year.\newlineB=$3,582×1.05B = \$3,582 \times 1.05
  6. Perform Multiplication: Perform the multiplication to find the final balance. \newlineB=$3,761.10B = \$3,761.10

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