Question

Please help!
Use your function to determine how much you will owe the bank in five years. This is assuming you are not paying down your loan, so do not get scared! Show all of your work.

Function: A(t) = 13,965 (1 + 03/12)^12t

Answer 1

@ganeshie8

Answer 2

@Luigi0210

Answer 3

@paki

Answer 4

@confluxepic

Answer 5

And this is what I have researched so far:

Answer 6

Alright! there is a mistake in your A(t) function. It should be :
\[\large A(t) = 13,965 \left(1 + \dfrac{0.03}{12}\right)^{12t}\]

Answer 7

for #6, simply plugin \(t=5\) in above function and use your calculator to get a numerical answer

Answer 8

Okay let me calculate that

Answer 9

I got 839994.75

Answer 10

Is that correct?

Answer 11

doesnt look correct, try again

Answer 12

you should get 16221.97..
http://www.wolframalpha.com/input/?i=13965%281+%2B+0.03%2F12%29%5E%2812*5%29

Answer 13

Oh wait, no I plugged it in wrong I got 16221.97 as well

Answer 14

Here are the last two questions

Answer 15

Being a smart financial planner, you want to figure out how many months it will be until you owe the bank an amount of $100,000,00. Solve for t and show all your work

Answer 16

good :) for #7 you need to solve \(t\) in below equation :
\[100,000 = 13,965 \left(1 + \dfrac{0.03}{12}\right)^{12t}\]

Answer 17

start by dividing \(13,965\) both sides

Answer 18

7.16 = (1 + 0.03/12) ^12t

Answer 19

Okay, what next?

Answer 20

Excellent! which is same as

\(\large 7.16 = (1.0025)^{12t}\)

taking \(\ln\) both sides you get
\(\large \ln (7.16) = \ln(1.0025)^{12t} \)

\(\large \ln (7.16) = 12t\ln(1.0025) \)

\(\large t = \dfrac{\ln (7.16) }{12\ln(1.0025)}\)

Answer 21

use your calculator to get a numerical answer ^

Answer 22

thats it! we're done with #7

Answer 23

So the answer for number 7 is 7.16 = (1.0025)^12t?

Answer 24

Or do I need to solve further?

Answer 25

@ganeshie8

Answer 26

But question number 8 is:

Answer 27

you need to solve further and find the time

Answer 28

first finish off #7

Answer 29

So would I divide ln (7.16) by 12ln (1.0025)

Answer 30

Exactly! that gives the time in years,
use your calculator

Answer 31

I got 7.14 Years, not sure if that is correct though

Answer 32

wolfram says t=65.699 years
http://www.wolframalpha.com/input/?i=ln+%287.16%29%2F%2812ln+%281.0025%29%29

Answer 33

multiply that by 12 to get the number of months it takes

Answer 34

Ah I see now, thank you! Okay, last question

Answer 35

Lastly, you decide to keep track of your loan four times a month instead of monthly. Solve for the adjusted interest rate. Remember to use the formula A(t)=P{(1+r/n)^1/c} where c = 4. When solving for the adjusted interest rate, be sure to set it equal to 1 + r/n

Answer 36

\[\large A(t) = 13,965 \left[1 + \dfrac{0.03}{12}\right]^{12t}\]

rewrite it as
\[\large A(t) = 13,965 \left[\left(1 + \dfrac{0.03}{12}\right)^{\frac{1}{4}}\right]^{4\times 12t}\]
\[\large A(t) = 13,965 \left[1.00062\right]^{48t}\]

Answer 37

which is same as

\[\large A(t) = 13,965 \left[1+0.00062\right]^{48t}\]

so \(\dfrac{r}{48} = 0.00062\)

solve \(r\) for the adjusted interest rate

Answer 38

I got r = 0.02976

Answer 39

@ganeshie8 would that be correct?