Martin has $3,582 in an account that earns 5% interest compounded annually.To the nearest cent, how much will he have in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.$□
Q. Martin has $3,582 in an account that earns 5% interest compounded annually.To the nearest cent, how much will he have in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.$□
Identify Given Values: Identify the given values from the problem.Principal p = $3,582Interest rate r = 5% or 0.05 when expressed as a decimalTime t = 1 yearWe will use the compound interest formulaB=p(1+r)t to find the balance after 1 year.
Substitute Values: Substitute the given values into the compound interest formula.B=($3,582)(1+0.05)1
Calculate Inside Parentheses: Calculate the value inside the parentheses.1+0.05=1.05
Raise to Power: Raise 1.05 to the power of 1, which is simply 1.05 since any number to the power of 1 is the number itself.1.051=1.05
Multiply Principal: Multiply the principal by the result from Step 4 to find the balance after 1 year.B=$3,582×1.05
Perform Multiplication: Perform the multiplication to find the final balance. B=$3,761.10