Question 1174220: An investment of $4950 earns 11%/a compounded semi-annually. How long will it take for the investment to grow to $9411? Found 3 solutions by greenestamps, ikleyn, Solver92311:Answer by greenestamps(13196) (Show Source):
The value after n compounding periods is the initial investment, multiplied by the periodic growth factor n times.
You want to know how long it will take the original $4950 to grow to $9411:
The variable is in an exponent; so to solve algebraically you need to use logarithms.
Use a calculator....
Or an easy path to the numerical answer is by graphing the two functions and on a graphing calculator and find that they intersect at n=12.
Then remember that n=12 is the number of compounding periods; since the compounding is twice a year, the length of time required for the investment to grow to $9411 is 12/2 = 6 years.
9411 = =
1.901212 =
log(1.901212) = 2t*log(1.055)
t = = 6.000022.
ANSWER. 6 years (rounded).
I hope that I safely rounded the value of 6.000022 to 6 and the last compounding will be done)
