Bobby and Shelley deposit $800.00 into a savings account which earns 6% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.Round your answer to the nearest cent.
Q. Bobby and Shelley deposit $800.00 into a savings account which earns 6% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.Round your answer to the nearest cent.
Identify values for P, r, and t: Identify the values for P, r, and t.Principal amount P = $800Rate of interest r = 6% or 0.06 when expressed as a decimal Time in years t = 3 years
Calculate final amount using continuous compounding interest formula: Use the continuous compounding interest formula A=Pert to calculate the final amount.Substitute P=800, r=0.06, and t=3 into the formula.A=800×e(0.06×3)
Calculate exponent part of the formula: Calculate the exponent part of the formula. 0.06×3=0.18
Calculate e raised to the power of 0.18: Calculate e raised to the power of 0.18.e0.18≈2.718280.18≈1.1972173...
Multiply principal amount by e0.18 to find final amount: Multiply the principal amount by the value of e raised to the power of 0.18 to find the final amount.A=800×1.1972173...A≈800×1.1972173≈957.77384
Round final amount to nearest cent: Round the final amount to the nearest cent. A≈$957.77
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