If Php 56,734 is the present value of P hp 254,652 when will it earn its interest if money is worth 10.25% compound quartely ?

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- anonymous

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- mathmate

@jacalneaila
I thought you're doing statics, suddenly you're in finite math? lol

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## More answers

- anonymous

im done in statics :)

- anonymous

thank you very much :)

- mathmate

Well, this is an application of the compound interest formula.
Are you familiar with the compound interest formula?

- anonymous

yes :)

- anonymous

can you check my answer :)

- mathmate

sure, what do you get, and how did you get it?

- anonymous

F=P(\[F=P(1+r/m)^t^m\]

- mathmate

Good, what you you use for r and m?

- anonymous

\[254,652=56734(1+10.25%/4)^(4)(x) \]

- anonymous

m=4

- anonymous

r=10.25%

- anonymous

date is missing

- anonymous

the answer is 14.84

- mathmate

Can you continue the formula from here?
254,652=56734(1+10.25

- anonymous

\[254,652=56734(1+10.25%/4)^(x)(4)\]

- anonymous

254,652=56734(1+10.25%/4)^(x)(4)

- anonymous

@mathmate 254,652=56734(1+10.25%/4)^(x)(4)

- mathmate

Try not to write the %, and the brackets at the end are not correct.
It should look like this.
254,652=56734(1+0.1025/4)^(4x)
How did you solve for x?

- anonymous

14.84

- anonymous

i put in calcu , shift solve

- mathmate

What kind of calculator solves this problem the way you entered it?

- anonymous

i use 991es calcu

- mathmate

Amazing, did it give more than two places of decimals? What's the rest of the number, if you have it?

- anonymous

yeass

- mathmate

Just curious, what's the rest of the numbers? (i.e. more accuracy for the answer?)

- anonymous

just put a x in calcu

- anonymous

althought , you have to adjust the decimal numbers

- mathmate

The problem is, 14.84 is not the correct answer, because you will see that
if you use the same compound interest formula, and solve for FV, you get PhP 254757.28 and not 254652. You need more accuracy.

- anonymous

the questions is when ? it means a date

- mathmate

That's ok if the answer satisfies your teacher!

- anonymous

i have also a problem with this questions

- anonymous

At what rate compounded monthly will php 36000 become php 48500 at the end of 85 months

- anonymous

in calcu , cant solve

- anonymous

@mathmate i use same formula , but icant solve

- mathmate

Can you post the formula the way you put it in and I can see why, or what we can do to make it solve?

- mathmate

The reason is you are not solving for the same unknown, you need some adjustments to help the calculator.

- anonymous

48500=36000(1+X/12)^(12)(85/12) rate is the missing

- mathmate

We will start by understanding how compound interest works, then we will be able to solve for anything, even when the 991es gets stuck, ok?

- anonymous

ok :)

- mathmate

So the compound interest formula works like this:
F=P(1+i/m)^(mt)
where F=future value, P=present value, m=number of times it compounds in a year, n=number of years, and i=(nominal) interest rate.
I think you are familiar with it, right?

- anonymous

48500=36000(1+x/12)^12 (85/12)?

- mathmate

Not too fast, we need to understand, and modify the formula to help the calculator. I was actually surprised that it found the answer the first time around!

- mathmate

Your formula is correct, but the problem is too hard for the calculator!

- mathmate

To continue our discussion, are you familiar with:
F=P(1+i/m)^(mt)
?

- anonymous

okay okay :) no

- anonymous

yes

- anonymous

yeah

- mathmate

But that's the same formula as the first AND second problem that you used!

- mathmate

ok, so you're familiar with it!

- anonymous

i will use it , wait :)

- mathmate

Are you able to solve for the period, using the formula, and not using the automatic solver of the calculator?

- anonymous

i will try :)

- mathmate

The key is to take log on both sides, which then reduces the exponentiation to a multiplication. See if you can come up with a new formula using logs!

- mathmate

without using the calculator, because we are not working with numbers!

- anonymous

:( , i did not get it

- mathmate

You're still using the calculator. I need you to take log on both sides of the formula, and simplify the equation. It will be in a form that the calculator will solve!

- mathmate

For now, ditch the calculator, and use pencil and paper!

- anonymous

how can i solve it

- anonymous

i have a pencil and paper

- anonymous

first step

- anonymous

how can u teach m

- anonymous

:(

- mathmate

Take log on both sides, and change the exponent (on the right of the equal sign) to multiplication, as the laws of exponents require.
log(ab)=log(a)+log(b)
log(a^b)= b log(a)
and put the modified formula for the calculator to solve.
Tell me what you get.

- mathmate

I got between 4 and 4.5 %.

- anonymous

i got 4.1254759065 x 10^-4

- mathmate

You seem to be a factor of approximately 10 off somewhere.
Use this interest rate and the compound interest formula to see you you get back 48500 after 85 months.
Can you show me what you put in the calculator, perhaps a 12 is missing or misplaced somewhere!

- mathmate

Using interest rate of 4.1254759065 x 10^-4, we get only 36105 after 85 monthes.

- mathmate

Try your calculator with
log(F/P)=log((1+x/12)^(12*85/12)

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