SOLUTION: Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.) Initial Investment: $900 Annual % Rate: UNKNOWN Time to Double (Year

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Question 1119112: Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Investment: $900
Annual % Rate: UNKNOWN
Time to Double (Years): UNKNOWN
Amount after 10 Years: $1305
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Initial Investment: $900
Annual % Rate: 3.716%
Time to Double (Years): 18.65 years
Amount after 10 Years: $1305



If using a model y=900e%5E%28kt%29, then value for the constant in the exponent is k=0.03716.

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
The model is  


y = 900*e^(k*t).


You are given that y = 1305 at t =10.  Write it as an equation:


1305 = 900*e^(k*10).


It is equivalent to  (after dividing both sides by 900):


1305%2F900 = e%5E%28k%2A10%29,   or   e%5E%28k%2A10%29 = 1.45.


Take the natural logarithm of both sides:


k*10 = ln(1.45)  ====>  10k = 0.37156  ====>  k = 0.37156%2F10 = 0.037156.


Thus the model is  y = 900%2Ae%5E%280.037156%2At%29.


Time to double:


1800 = 900%2Ae%5E%280.037156%2At%29  ====>  


2 = e%5E%280.037156%2At%29.


Take the natural logarithm of both sides:


ln(2) = 0.037156*t  ====>  t = ln%282%29%2F0.037156 = 0.69315%2F0.037156 = 18.65 years.


Answer. Annual rate is  e%5E0.037156 = 1.038.

        Equivalent annual percentage rate is 3.8% (considered as annually compounded)

        Time to double is 18.65 years.