SOLUTION: How long will it take Php 2000 to earn Php 500 if the interest is 12% compound monthly

Question 1188726: How long will it take Php 2000 to earn Php 500 if the interest is 12% compound monthly
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the interest is 12% compounded monthly.
diviee that by 12 to get an interest of 1% per month.
divide that by 100 and add 1 to it to get a growth rate of 1.01 per month.
to earn an interest of 500, the 2000 must grow to 2500.
your equation is 2500 = 2000 * 1.01 ^ n
n is the number of months.
divide both sides of that equation by 2000 to get:
2500 / 2000 = 1.01 ^ n
simplify to get:
5/4 = 1.01 ^ n
take the log of both sides of the equation to get:
log(5/4) = log(1.01 ^ n) which becomes:
log(5/4) = n * log(1.01)
divide both sides of that equation by log(1.01) to get:
log(5/4) / log(1.01) = n
solve for n to get:
n = 22.42574188

it will take 22.42574188 months to earn 500 interest on the account.
2000 * 1.01 ^ 22.42574188 = 2500
2500 - 2000 = 500 interest.

Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.

It will take 23 months, precisely and exactly.

You can not accept 22.43 months from the solution by @Theo.

You must round it to the closest greater month, which is 23 months, in order for
the bank was in position to make the last compounding.

23 months is your correct answer.

22.43 months is not enough.

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

To see many other similar and different problems solved, look into these two lessons
    - Compounded interest percentage problems
    - Problems on discretely compound accounts
in this site, and learn the subject from there.

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

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.

Happy learning ( ! )

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