Question

How do I go about solving this complex compound interest problem with a variable?

Answer 1

\[50000=20000(1+\frac{ x }{ 12})^{25}\]

Answer 2

The first step is to divide both sides by 20,000

Answer 3

Doing that and then flipping the two sides gives you

\[\Large \left(1+\frac{ x }{ 12}\right)^{25} = 2.5\]

Answer 4

The next step is to raise both sides to the power 1/25

this will cancel out the exponent of 25 on the left side of my equation above (since 25*(1/25) = 1)

So we'll have

\[\Large 1+\frac{ x }{ 12} = (2.5)^{1/25}\]

Answer 5

do you see how to finish up?

Answer 6

yeah, that makes a ton of sense :O!!!! Thanks!!!

Answer 7

Think you can help with one more :'O?

Answer 8

sure go ahead

Answer 9

\[50000=20000(1+\frac{ 0.0315 }{ 12})^{12*x}\]

Answer 10

what is your first step

Answer 11

Divide by 20000 so I end up with...\[2.5=(1+\frac{ 0.0315 }{ 12 })^{12*x}\]

Answer 12

good

Answer 13

now the next step is to somehow isolate that exponent 12x

we use logs to do this

Answer 14

apply the log base 10 to both sides

\[\Large \log(2.5)=\log\left((1+\frac{ 0.0315 }{ 12 })^{12*x}\right)\]

doing this allows us to pull down the exponent 12x

\[\Large \log(2.5)=12x*\log\left(1+\frac{ 0.0315 }{ 12 }\right)\]

what's next?

Answer 15

\[0.4=12x+0.0114\]

Answer 16

Right...?

Answer 17

not quite

Answer 18

1+0.0315/12 = 1.002625

the log of that is log(1.002625) = 0.00113852934813 which is roughly 0.00114 which is what you got

Answer 19

however, it should be 12x*0.00114 on the right side

Answer 20

also, on the left side, I would use at least 3 decimal digits of accuracy

Answer 21

what I got so far is

0.3979 = 12x*0.0011385

do you see how to finish up?

Answer 22

x=29.12458?

Answer 23

About?

Answer 24

yes approximately

Answer 25

Ah ok! That makes a lot of sense!

Answer 26

I really can't thank you enough, you really explained it in a very understandable way.

Answer 27

I'm glad things are clicking now