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 ?

Question

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 ?

anonymous · Answer

@mathmate

anonymous · Answer

@mathmate

mathmate · Answer

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

anonymous · Answer

im done in statics :)

anonymous · Answer

thank you very much :)

mathmate · Answer

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

anonymous · Answer

yes :)

anonymous · Answer

can you check my answer :)

mathmate · Answer

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

anonymous · Answer

F=P($$F=P(1+r/m)^t^m$$

mathmate · Answer

Good, what you you use for r and m?

anonymous · Answer

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

anonymous · Answer

m=4

anonymous · Answer

r=10.25%

anonymous · Answer

date is missing

anonymous · Answer

the answer is 14.84

mathmate · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

mathmate · Answer

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 · Answer

14.84

anonymous · Answer

i put in calcu , shift solve

mathmate · Answer

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

anonymous · Answer

i use 991es calcu

mathmate · Answer

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

anonymous · Answer

yeass

mathmate · Answer

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

anonymous · Answer

just put a x in calcu

anonymous · Answer

althought , you have to adjust the decimal numbers

mathmate · Answer

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 · Answer

the questions is when ? it means a date

mathmate · Answer

That's ok if the answer satisfies your teacher!

anonymous · Answer

i have also a problem with this questions

anonymous · Answer

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

anonymous · Answer

in calcu , cant solve

anonymous · Answer

@mathmate i use same formula , but icant solve

mathmate · Answer

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 · Answer

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

anonymous · Answer

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

mathmate · Answer

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 · Answer

ok :)

mathmate · Answer

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 · Answer

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

mathmate · Answer

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 · Answer

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

mathmate · Answer

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

anonymous · Answer

okay okay :) no

anonymous · Answer

yes

anonymous · Answer

yeah

mathmate · Answer

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

mathmate · Answer

ok, so you're familiar with it!

anonymous · Answer

i will use it , wait :)

mathmate · Answer

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

anonymous · Answer

i will try :)

mathmate · Answer

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 · Answer

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

anonymous · Answer

:( , i did not get it

mathmate · Answer

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 · Answer

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

anonymous · Answer

how can i solve it

anonymous · Answer

i have a pencil and paper

anonymous · Answer

first step

anonymous · Answer

how can u teach m

anonymous · Answer

:(

mathmate · Answer

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 · Answer

I got between 4 and 4.5 %.

anonymous · Answer

i got 4.1254759065 x 10^-4

mathmate · Answer

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 · Answer

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

mathmate · Answer

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