SOLUTION: Find the time required for an investment of 5000 dollars to grow to 9000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Question 1199357: Find the time required for an investment of 5000 dollars to grow to 9000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
f = p * (1+r) ^ n
f is the future value
p is the present value
(1+r) is the growth factor per time period
r is the growth rate per time period
n is the number of time periods

in this problem, you get:
9000 = 5000 * (1+.075/4) ^ n
simplify to get:
9000 = 5000 * 1.01875 ^ n
divide both sides of the equation by 5000 and simplify to get:
9/5 = 1.01875 ^ n

take the log of both sides of the equation to get:
log(9/5) = log(1.01875 ^ n)
this becomes log(9/5) = n * log(1.01875) by the log rule that says that log(x^n) = n * log(x).
divide both sides of the equation by log(1.01875) to get:
log(9/5) /log(1.01875) = n
solve for n to get:
n = 31.64160555 quarters of a year.
divide that by 4 to get:
n = 7.910401388 years.

you could have used a calculator such as the one found at https://arachnoid.com/finance/ to get the same answer.

the inputs to that calculator were:
pv = -5000 (negaive because it's money you invested.
fv = 9000 (positive because it's money you got back in treturn after the investment period).
np = what you want to find.
pmt = 0 because there is no payment per time period.
ir = quarterly interest rate = 7.5 / 4 = 1.875%
payment mad at the end or the beginning of the time period isn't used because there is no payment per time period.
you click on np and the calculator tells you the number of time periods.

here are the results from using that cslculator.

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

The solution, the answer and the logic in the post by @Theo all are incorrect.

To be correct, the number n = 31.64160555 of quarters of a year be rounded to the closest
larger integer, which is 32 quarters, or 8 years.

It be rounded in order for the bank was in position to make the last compounding.

such rounding, the in the post by @Theo is simply .

Do not repeat his error.

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To see many similar problems, solved correctly, look into the lesson
    - Problems on discretely compound accounts
in this site, and learn the subject from there.

After reading this lesson, you will tackle such problems on your own without asking for help from outside.

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