QuestionJune 17, 2025

Suppose your great-great grandfather invested 800 earning 5.5% interest compounded continuously 100 years ago. How much would his investment be worth today? Today his investment will be worth square (Do not round until the final answer. Then round to two decimal places as needed.)

Suppose your great-great grandfather invested 800 earning 5.5% interest compounded continuously 100 years ago. How much would his investment be worth today? Today his investment will be worth square (Do not round until the final answer. Then round to two decimal places as needed.)
Suppose your great-great grandfather invested 800 earning 5.5%  interest compounded continuously 100 years ago. How much would his investment be
worth today?
Today his investment will be worth square 
(Do not round until the final answer. Then round to two decimal places as needed.)

Solution
4.5(325 votes)

Answer

\15,356.26 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**, where P is the principal amount, r is the interest rate, and t is the time in years. 2. Substitute values into the formula Given P = 800, r = 0.055, and t = 100. Substitute these values into the formula: A = 800 \cdot e^{0.055 \cdot 100}. 3. Calculate the exponent Compute the exponent: 0.055 \times 100 = 5.5. 4. Evaluate the exponential expression Calculate e^{5.5} using a calculator or computational tool. 5. Compute the final amount Multiply the result by 800 to find A: A = 800 \cdot e^{5.5}. 6. Round the final answer Round the calculated value of A to two decimal places.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**, where $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time in years.<br /><br />2. Substitute values into the formula<br /> Given $P = 800$, $r = 0.055$, and $t = 100$. Substitute these values into the formula: $A = 800 \cdot e^{0.055 \cdot 100}$.<br /><br />3. Calculate the exponent<br /> Compute the exponent: $0.055 \times 100 = 5.5$.<br /><br />4. Evaluate the exponential expression<br /> Calculate $e^{5.5}$ using a calculator or computational tool.<br /><br />5. Compute the final amount<br /> Multiply the result by 800 to find $A$: $A = 800 \cdot e^{5.5}$.<br /><br />6. Round the final answer<br /> Round the calculated value of $A$ to two decimal places.
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