An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-t)dt = 15.000 e0.08(N -t)dt Integrate with respect to t. 15,000 e 0.08(N-t)dt = - 187.500 e0.08(N - 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 - 187,500 e0.08(N - t)N - 187,500 (e0- 0.08N) = 150,000 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.
An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-t)dt = 15.000 e0.08(N -t)dt Integrate with respect to t. 15,000 e 0.08(N-t)dt = - 187.500 e0.08(N - 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 - 187,500 e0.08(N - t)N - 187,500 (e0- 0.08N) = 150,000 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.
Transcribed Image Text:An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000?
The amount of time required is approximately years.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
View an Example
Question Help
An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000,
how much time is required until the value of the investment reaches $150,000?
KeN-)dt =15,000 e
,0.08(N-t)dt
r(N
Integrate with respect to t.
15,000 e e0.08(N - t)
0.08(N-1) dt = - 187,500
0.08(N – 1)|
Now, set the definite integral equal to the ending balance and isolate the exponential term.
= 150,000
%3D
-187,500 e0.08(N-1)
- 187,500 (e- e0.08N)
= 150,000
%3D
0.08N = 1.8
Take the natural logarithm of both sides and solve for N.
0.08N = 1.8
0.08N = In (1.8)
N 7.35
The amount of time required is approximately 7.35 years.
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