Question 1188721: if you deposit Php 8000 into an account paying 7% aanual interest compounded quarterly, how long until is Php 12400 in your account
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 7% annual interest compounded quarterly is equal to (7/4)% per quarter.
(7/4)% = 1.7% each quarter.
divide that by 100 to get a rate of .0175 and add 1 to it to get a growth rate of 1.0175 per quarter.
you want to know how long before your money reaches 12400.
1.55 = 1.0175 ^ x, where x represents the number of quarters.
take the log of both sides of this equation to get:
log(1.55) = log(1.0175 ^ x).
since log(1.0175 ^ x) is equal to x * log(1.0175), this becomes:
log(1.55) = x * log(1.0175).
divide both sides of the equation by log(1.0175) to get:
log(1.55) / log(1.0175) = x
solve for x to get:
x = 25.26163279.
that's how many quarters of a year it will take.
divide that by 4 to get:
x = 6.315408196 years.
confirm by solving for y = 8000 * 1.0175 ^ 25.26163279 to get:
y = 12400.
the equation that i worked from 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.
you were given the rate per year of 7%.
divide that by 100 to get .07 per year.
divide that by 4 to get .0175 per quarter.
your time periods are in quarters of a year.
the equation became:
12400 = 8000 * (1 + .0175) ^ n
divide both sides of the equation by 8000 to get:
12400 / 8000 = (1 + .0175) ^ n
take the log of both sides of the equation to get:
log(12400 / 8000) = log((1 + .0175) ^ n) which becomes:
log(12400 / 8000) = n * log(1 + .0175).
divide both sides fo log(1 + .0175) to get:
log(12400 / 8000) / log(1 + .0175) = n
solve for n to get:
n = 25.26163279.
sine the time periods were in quarters of a year, then the solution is 25.26163279 quarters of a year, which, when divided by 4, gives you the number of years.
Answer by ikleyn(52847)  (Show Source):
You can put this solution on YOUR website! .
if you deposit Php 8000 into an account paying 7% annual interest compounded quarterly,
how long until is Php 12400 in your account ?
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It will take 26 quarters, precisely and exactly, which is 6 years and half.
You can not accept 25.26 quarters from the solution by @Theo.
You must round it to the closest greater quarter, which is 26 quarters, in order for
the bank was in position to make the last compounding.
26 quarters is your correct answer.
25.26 quarters is not enough.
@Theo REPEATS HIS ERROR just, probably, more than 10 times in this forum,
ALTHOUGH and DESPITE I corrected and taught him all the time.
-------------------
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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