Question 5
An investment of $\$ 59.600 .00$ earns $20 \%$ annual interest, compounded continuously. If no funds are added or removed from this account: what is the future value of the investment after 12 years? Round your answer to the nearest pernin.
Future value $=$ \$
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Answer
\(\boxed{A = $656,981.32}\)
Step 1 ：Given the principal amount (P) as $59,600.00, the annual interest rate (r) as 20% or 0.20 in decimal, and the time (t) as 12 years.
Step 2 ：The formula for continuous compounding is \(A = P * e^{rt}\), where A is the amount of money accumulated after n years, including interest.
Step 3 ：Substitute the given values into the formula: \(A = $59,600.00 * e^{0.20 * 12}\)
Step 4 ：Simplify the exponent: \(A = $59,600.00 * e^{2.4}\)
Step 5 ：Using the value of e (approximately 2.71828), calculate the value: \(A = $59,600.00 * 11.02317638\)
Step 6 ：\(\boxed{A = $656,981.32}\)
