Question

Sal currently has an account balance of $2,835.48. He opened the account five years ago with a deposit of $2,310.72. If the interest compounds twice a year, what is the interest rate on the account? Multiple Choice : 2.1%

4.1%

5.9%

8.4%

Answer 1

Remember that formula from before?

\[\large A = P(1 + \frac{ r }{ n })^{nt}\]

Well this time..we have

A = $2,835.48
P = 2,310.72
N = 2
and
T = 5

so we plug everything in..and we get...

\[\large 2835.48 = 2310.72(1 + \frac{ r }{ 2 })^{2 \times 5}\]

Can you solve for 'r' ...?

Answer 2

I dont understand the process of the r? can you please explain..

Answer 3

do i multiply like cross multiply?

Answer 4

or can i put a number representing r?

Answer 5

do i plug in each rate and then see if it gives me the answer?

Answer 6

Sorry about that I was away...

Okay well...you CAN do that if you really want to...but a better way would be to rearrange this equation for 'r'

First...divide both sides by 2310.72....What do we have after that?

Answer 7

okay hold on let me divide

Answer 8

so i divide the left side? now?

Answer 9

You divide both sides by the 2310.72

\[\large \frac{ 2835.48 }{ 2310.72 } = \frac{ 2310.72(1 + \frac{ r }{ 2 })^{10} }{ 2310.72 }\]

like that...

Answer 10

yes thats what i did and i scratched out the 2310.72 from the right side since it crosses out right?

Answer 11

Correct...

Answer 12

now i got 1.227098047 for the left side is that fine?

Answer 13

Yeah we can keep all those numbers....it'll come out pretty much to the same number at the end...

Okay so now we have

\[\large 1.227098047 = (1 + \frac{r}{2})^{10} \]

Now I think it would be easier to just take the 10th root of both sides...like \(\large \sqrt[10]{n} \)

Like that of both sides....so lets do that...

\[\large \sqrt[10]{1.227098047} = \sqrt[10]{(1 + \frac{r}{2})^{10}} \]

What does this simplify out to...?

Answer 14

okay let me try this

Answer 15

left 11.07744577

Answer 16

do we cross out the 10's in the right side?

Answer 17

We're going to have to do the left side again but yes the "10's" cancel out on the right...

Answer 18

\[\huge \sqrt[10]{1.227098047} = 1.0206760553\]

Does that look right??

Answer 19

no ?

Answer 20

im so sorry im just really confused sorry sorry

Answer 21

Well remember we are asking ourselves "what number times itself 10 times....= the 1.227098047

This comes out to what I posted....wait are you using a calculator?

Answer 22

yes

Answer 23

I know exactly what you did...you wrote

\[\huge 10\sqrt{1.227098047}\]

What this does.....is take the SQUARE ROOT of the number...then multiply it by 10...

What that needs to be is...

\[\huge \sqrt[10]{1.227098047}\]

try typing that in google if you need to..."tenth root of 1.227098047"

Answer 24

it says its the answer you got before

Answer 25

1.02067605529

Answer 26

Right....so that is something you have to watch our for when doing these with your calculator...

Okay so now we have:

\[\large 1.02067605529 = 1 + \frac{ r }{ 2 }\]

Now remember our GOAL is to isolate 'r'...so lets subtract 1 from both sides of the equation...

what do we have now?

Answer 27

.020676055 left r/2 right

Answer 28

That is correct...and how do we finish solving for 'r'...?

Answer 29

we divide by 2

Answer 30

i mean multiply

Answer 31

Not quite..rememb.....

nvm you caught it lol..yes multiply both sides by 2...

Answer 32

but its not giving the correct answer ...

Answer 33

You'll see in a second...post what you got...

Answer 34

0.04135211=r

Answer 35

Right...now

Remember your last question when I said...to convert from a percent to a decimal..you put the number over 100?

Well to convert from a decimal to a percent...you MULTIPLY by 100..

so now you get...?

Answer 36

ohhhhh 4.1

Answer 37

There you go! :)

Answer 38

Thank you so much would you mind helping me with one more?

Answer 39

Oh geez another one >.> haha no just kidding....yeah go ahead and post it :)

Answer 40

Thanks

Answer 41

Ramona deposited $4,190.51 into a savings account with an interest rate of 5.2% compounded twice a year. About how long will it take for the account to be worth $9,000?

33 years, 5 months

29 years, 9 months

14 years, 11 months

20 years, 8 months

Answer 42

I think its c but im not sure this is a guess

Answer 43

so can you explain in depth because.. yeah lol

Answer 44

Lol well okay...first ...Same formula...and lets plug in your values...

\[\large 9000 = 4190.51(1 + \frac{ .052 }{ 2 })^{2t}\]

Alright...so how did we start off the last problem? what would be step 1?

Answer 45

divide by 4190.51

Answer 46

Right...

Answer 47

2.15 left

Answer 48

(1+.052/2)^2t

Answer 49

Okay so...

*lets just keep it exact....

2.1477 left...

so

\[\large 2.1477 = (1 + \frac{ .052 }{ 2 })^{2t}\]

Now do what's inside of the parenthesis..what do you get from that?

Answer 50

2.1477(1.026)^2t

Answer 51

Remember the '=' sign inbetween those...but yes..

\[\large 2.1477 = (1.026)^{2t}\]

Now...I take it you have gone over "logs" before?

Answer 52

i honestly dont remember logs

Answer 53

your probs gunna kill me sorry

Answer 54

yeah i checked over my work and its 14 and 11 months

Answer 55

thanks though you were much help :)

Answer 56

Im so sorry for all teh questions and im dumb slow brain
Im really bad at math

Answer 57

Alright...well I'll show you what to do lol....but remember to go over those :)

When you take the natural log (ln) of both sides of this equation...it allows you to bring the exponent containing the variable down in front of the term...

aka

\[\large 1.026^{2t}\]

after taking the natural log we have

\[\large 2t \times \ln (1.026)\]

And remember we have to do it to the other side as well...so altogher we have

\[\large \ln (2.1477) = 2t \times \ln(1.026)\]

*just remember to look over those again okay?

Answer 58

lol I didn't see everything you posted lol...yes it does come out to 14 and 11 months....well good work!