SOLUTION: A firm decided to increase its output from its current level of 60,000 to 70,000. Assume that the compounded interest required to achieve this growth is 10%. Find the number of ye

Question 1159780: A firm decided to increase its output from its current level of 60,000 to 70,000. Assume that the
compounded interest required to achieve this growth is 10%. Find the number of years needed to
reach the required output.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
compound interest formjla is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
in your problem:
p = 60,000
f = 70,000
r = 10% per year.
n = number of years.
formula becomes 70,000 = 60,000 * (1 + .10) ^ n
divide both sides of this equation by 60,000 to get:
70,000 / 60,000 = (1 + .10) ^ n
simplify to get:
7/6 = 1.1 ^ n
take the log of both sides of this equation to get:
log(7/6) = log(1.1^n)
since log(1.1^n) = n * log(1.1), the equation becomes:
log(7/6) = n * log(1.1)
solve for n to get:
n = log(7/6) / log(1.1) = 1.617357979 years
60,0000 output will increase to 70,000 output in that many years.
confirm by replacing n in the original formula with that to get:
f = 60,000 * 1.1 ^ 1.617357979 = 70,000.
this confirms the solution is correct, assuming the correct formula was used.
Answer by ikleyn(53751) (Show Source): You can put this solution on YOUR website!
.

The correct answer is

Under given conditions, the number of years needed to reach the required output is 2 years. Since compounding is made at the end of an year, ONLY.

---------------

By the way, the condition says NOTHING about the compounding time period, so

(a) it is the problem's FAULT, and (b) BY DEFAULT, the compounding period is 1 year.

/\/\/\/\/\/\/\/

As the problem is worded, it is BAD STYLE writing Math problem;

besides of it, there are deficiencies in its formulation, from the common sense of view.

(It is my personal opinion).

It is better do not go to the public with problems, formulated in this way.

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