Question

MATH HELP ! Medals will be given !

Answer 1

Pierre deposited 9,875 into a savings account 23 years ago. The account has a interest rate of 2.7% and the balance is currently 18,374.86. How often does the interest compound?

Answer 2

@satellite73

Answer 3

@pathosdebater

Answer 4

wow ok i bet we can do this

Answer 5

\[18,374.86.= 9,875(1+\frac{.027}{n})^{23n}\] and some how we need to solve for \(n\)

Answer 6

After this question can you check my answers on my other questions please

Answer 7

What do we do to solve for n

Answer 8

divide by \(9875\) first

Answer 9

actually, the first thing i would do would be guess
lets guess monthly and see if it is right

Answer 10

Ok so divide what to what ?

Answer 11

hmm very close

Answer 12

I'm still lost

Answer 13

@satellite73 I was about to solve it but then again, there is a "n" inside the brackets which makes simplifying a little harder than I thought. You COULD use newton's method on it which is a repetitive formula for finding the zeroes of any function using derivatives from calculus...I'm just thinking if there is a algebraically simpler way...

Answer 14

...hmm

Answer 15

start here
\[18,374.86= 9,875(1+\frac{.027}{n})^{23n}\] and then divide both sides by \(9875\) to get
\[\frac{18374.86}{9875}=(1+\frac{.027}{n})^{23n}\]

Answer 16

oh damn, the method i was trying will not work
i think it is better to guess and check

Answer 17

Yeah but then even with using logarithms...it is still pretty complex

Answer 18

is it annually

Answer 19

really?!

Answer 20

huh ?

Answer 21

no actually it is not annually because
\[9875(1.027)^{23}=18224.57\]

Answer 22

http://www.wolframalpha.com/input/?i=9875%281.027%29^23

Answer 23

its quarterly

Answer 24

ok lets try that

Answer 25

ok

Answer 26

\[9875(1+\frac{.07}{4})^{4\times 23}=18336.98\]
http://www.wolframalpha.com/input/?i=9875%281%2B.027%2F4%29^%284*23%29

Answer 27

i made a typo there, but the wolfram answer is correct

Answer 28

so was i right ?

Answer 29

no that is too small by a little

Answer 30

here is monthly
http://www.wolframalpha.com/input/?i=9%2C875%281%2B.027%2F12%29^%2812*23%29

Answer 31

danngit. i can't be daily

Answer 32

we can try daily

Answer 33

http://www.wolframalpha.com/input/?i=9%2C875%281%2B.027%2F365%29^%28365*23%29

Answer 34

looks like we have a winner!

Answer 35

Hmmmm, DAILY :)

Answer 36

go with daily

Answer 37

nothing like a little guess and check

Answer 38

is it daily 100%

Answer 39

According to wolfram alpha,
\[n\phantom{.}\dot{=}\phantom{.}0.00746783522465871\]

Answer 40

so what do you think it is @KeithAfasCalcLover daily ?

Answer 41

it is daily because we checked it

Answer 42

Well im not sure, ahah I was just solving the equation was given.

Answer 43

I have to be honest, I never liked financial applications. I tried to focus on the equation solving part.