Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Bobby and Shelley deposit $800.00\$800.00 into a savings account which earns 6%6\% interest compounded continuously. They want to use the money in the account to go on a trip in 33 years. How much will they be able to spend?\newlineUse the formula A=PertA = Pe^{rt}, where AA is the balance (final amount), PP is the principal (starting amount), ee is the base of natural logarithms (2.71828\approx 2.71828), rr is the interest rate expressed as a decimal, and tt is the time in years.\newlineRound your answer to the nearest cent.

Full solution

Q. Bobby and Shelley deposit $800.00\$800.00 into a savings account which earns 6%6\% interest compounded continuously. They want to use the money in the account to go on a trip in 33 years. How much will they be able to spend?\newlineUse the formula A=PertA = Pe^{rt}, where AA is the balance (final amount), PP is the principal (starting amount), ee is the base of natural logarithms (2.71828\approx 2.71828), rr is the interest rate expressed as a decimal, and tt is the time in years.\newlineRound your answer to the nearest cent.
  1. Identify values for P, r, and t: Identify the values for P, r, and t.\newlinePrincipal amount PP = $800\$800 \newlineRate of interest rr = 6%6\% or 0.060.06 when expressed as a decimal \newlineTime in years tt = 33 years
  2. Calculate final amount using continuous compounding interest formula: Use the continuous compounding interest formula A=PertA = Pe^{rt} to calculate the final amount.\newlineSubstitute P=800P = 800, r=0.06r = 0.06, and t=3t = 3 into the formula.\newlineA=800×e(0.06×3)A = 800 \times e^{(0.06 \times 3)}
  3. Calculate exponent part of the formula: Calculate the exponent part of the formula. 0.06×3=0.180.06 \times 3 = 0.18
  4. Calculate ee raised to the power of 0.180.18: Calculate ee raised to the power of 0.180.18.e0.182.718280.181.1972173...e^{0.18} \approx 2.71828^{0.18} \approx 1.1972173...
  5. Multiply principal amount by e0.18e^{0.18} to find final amount: Multiply the principal amount by the value of ee raised to the power of 0.180.18 to find the final amount.\newlineA=800×1.1972173...A = 800 \times 1.1972173...\newlineA800×1.1972173957.77384A \approx 800 \times 1.1972173 \approx 957.77384
  6. Round final amount to nearest cent: Round the final amount to the nearest cent. A$957.77A \approx \$957.77

More problems from Continuously compounded interest: word problems