The Sharma's earn $\$ 12000$ per year on their small internet business. If this is viewed as a continuous income stream, how much would this money accrue to in 7 years at $3.95 \%$ interest compounded continuously?
Round your answer to the nearest dollar and do not use commas in the answer blank.
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Answer
The final amount accrued in 7 years at \(3.95\%\) interest compounded continuously is \(\boxed{15822}\)
Step 1 ：Use the formula for continuous compounding interest: \(A = P \cdot e^{rt}\)
Step 2 ：Let \(P = 12000\), \(r = 0.0395\), and \(t = 7\)
Step 3 ：Calculate the amount accrued: \(A = 12000 \cdot e^{0.0395 \cdot 7}\)
Step 4 ：Round the final answer to the nearest dollar: \(A \approx 15822\)
Step 5 ：The final amount accrued in 7 years at \(3.95\%\) interest compounded continuously is \(\boxed{15822}\)
