SOLUTION: 1. A university invests $100,000 into an account that pays a 4.75% annual rate compounded continuously. Using the formula A=Pert, where A=the amount in the account after t years, P

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1. A university invests $100,000 into an account that pays a 4.75% annual rate compounded continuously. Using the formula A=Pert, where A=the amount in the account after t years, P      Log On


   

Question 1163680: 1. A university invests $100,000 into an account that pays a 4.75% annual rate compounded continuously. Using the formula A=Pert, where A=the amount in the account after t years, P=principal invested, and r=the annual interest rate, how many years, to the nearest tenth, will it take for the university's investment to double?
b) to triple?
c) to quadruple?
Answer by ikleyn(52893) About Me  (Show Source):
You can put this solution on YOUR website!
.

Part  (a):   to double


200000 = 100000%2Ae%5E%280.0475%2At%29


200000%2F100000 = e%5E%280.0475%2At%29


2 = e%5E%280.0475%2At%29


It is your basic formula for doubling.


Take natural logarithm of both sides


ln(2) = 0.0475*t


t = ln%282%29%2F0.0475 = 14.59  years.    ANSWER

This case is completed.

For other cases do the same.   Part  (a)  is your  TEMPLATE  for other parts.

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To see the theory and many other similar solved problems,  see my lesson
    - Problems on continuously compounded accounts
in this site.

Consider this lesson as your textbook, handbook, tutorials and (free of charge) home teacher.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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