SOLUTION: When will P80,000 grow to P95,000 if it's invested at 4.5% compounded quarterly?

Question 1173001: When will P80,000 grow to P95,000 if it's invested at 4.5% compounded quarterly?
Found 2 solutions by priscilla591, ikleyn:
Answer by priscilla591(1)   (Show Source): You can put this solution on YOUR website!
t≈ 3.84 years

start by plugging the information provided within the question into the compound interest formula for n compounds per year: A=P(1 + r/n)^(nt), where:
A= Final Amount
P = Principal (initial investment)
r = APR (annual percent rate, decimal)
t = number of years
n = number of compounds per year
you should get: 95,000 = 80,000(1 + 0.045/4)^(4t)
steps:
start with 95,000 = 80,000(1 + 0.045/4)^(4t)
then add the values in the parentheses to get 95,000 = 80,000(1.01125)^(4t)
after that you divide both sides of the equation by 80,000 and get 19/16 = 1.01125^(4t)
then you can convert the decimal into a fraction -> (809/800)^(4t) = 19/16 (i swapped the two sides of the equation so you could see the where the arrow was pointing to)
after that, you take the logarithm of both sides of the equation and get 4t = log(base 809/800)(19/16)
finally divide both sides of the equation by 4 to get: t = 1/4 log(base 809/800)(19/16)
you should have access to a calculator for this so you can input t = 1/4 log(base 809/800)(19/16) into the calculator and it will give you
t ≈3.84034 which you could also round to 4 years
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

a   TWIN   problem was just solved 20 minutes ago under this link

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1173000.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1173000.html

The approach used in this solution is similar to that of Priscilla, but is much more STRAIGHTFORWARD and SIMPLE,
since it uses logarithm base 10, instead of (unjustly) complicated logarithm's base of the Priscilla' solution.

So, learn my referred solution and try to adopt it.

Notice that my approach using logarithm base 10 is the STANDARD method solving such problems.

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

Priscilla, please accept my congratulations with your debut at this forum.

It can be useful for you, TOO, to be acquainted with my solution and the lesson, to which I referred in my post.

Priscilla, it is nice that you love to teach others; and I see that you have good skills and incline to explain,

but at this forum, you also may learn   A LOT   for yourself.

Do not miss this opportunity (!)

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