Question 1159780
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.