Question

Margaret currently has a balance of $7,726.99 in an account earning simple interest. Sixteen years ago she opened the account with an initial deposit of $5,278. What is the interest rate on this account?

Answer 1

There is the annual compounding equation that looks like
FV = PV(1+i)^n
where
FV = future value [given above]
PV = present value [given above]
n = number of years [given above]
i = interest rate [what we are solving for]

make sense now?

Answer 2

Kinda so it would be
7,726.99=5,278(1+i)^16??

Answer 3

@Hero

Answer 4

Looks right. Solve for i

Answer 5

this is were I get confused.

Answer 6

Divide both sides by 5,278 then radical both sides to the 16th root.

Answer 7

so 5,278/7,726.99=0.683060 raise that to the 16th and you get 0.00224566

Answer 8

I'm pretty sure you did something wrong there.

Answer 9

I have no idea what im doing wrong I didn't get much practice in on this

Answer 10

would I multiply the interest by the PV?

Answer 11

After taking the 16th root of both sides, I get

1.02411 = 1 + i

then subtracting 1 from both sides:

1.02411 - 1 = i
1.02411- 1 = i
0.02411 = i

Answer 12

so the interest would be 2.4%? or would I plug in that to the equation?

Answer 13

The annual interest rate is 2.4%

But for the equation, i = 0.02411

Answer 14

I remember I was taught to solve these using logs. So dumb when you can just take the nth root of both sides.

Answer 15

so the new equation would be 7,726.99=5,278(1+0.02411)^16??

Answer 16

Yes

Answer 17

I had no time to learn how to do this any other way because I have to take part A and part B this semester it sucks.

Answer 18

If they make you use logs, you're screwed.

Answer 19

I remember using logs in other math classes it sucked hopefully I don't have to.

Answer 20

so part 1 would be
7,726.99=5,278(1.02411)^16th

Answer 21

I only have one rule: Avoid logs whenever possible.

Answer 22

then that would become 7,726.99=5,278(1.464)

Answer 23

after this would I multiply 5278 by 1.464?

Answer 24

If you're trying to check the result, you can do that, but it's not necessary in this case if you did your algebra correctly. The main thing is making sure the equation used is appropriate for this problem. There are a lot of PV and FV equations out there. It is easy to use one thinking it is the right one just because all the numbers fit and you can solve for the requested variable. But just because you can solve for the requested variable doesn't mean the right equation was used.

Answer 25

i don't think we used the right one because i did multiply that and got the FV but that percentage is not one of my answers. my answers are
2.0%
9.2%
2.9%
6.3%

Answer 26

Let me see what happens if I use logs

Answer 27

If I get a different result with logs, then you have no choice but to learn logs.

Answer 28

would it be possible to plug in each percent into the equation and try to get the answer that way?

Answer 29

You could try that, but if the equation is wrong to begin with, it would be useless.

Answer 30

Also, doing that would work for multiple choice, but if you run into a problem where you have to solve it without multiple choice, you're stuck.

Answer 31

(1+0.02)^16=1.3727
multiply that by 5278 and you would get 7245 that one is wrong

Answer 32

2.9 is wrong as well

Answer 33

There's no way to solve it with logs. Well, actually, there is, if you let
b = 1 + i

Answer 34

i think the formula is \[7,726.99=5,278\( 1+\frac{ R }{ i } )^{t-1}\]

Answer 35

Where did you get that from? It doesn't look right

Answer 36

this formula is for compound interest

Answer 37

The other formula was for compound interest

Answer 38

A=p(1+r/n)^rt

Answer 39

I think you mean

A = p(1 + r/n)^nt

Answer 40

It comes out to the exact same thing.

Answer 41

Because n = 1

Answer 42

So you would end up with the exact same equation if you used compound interest.

Answer 43

And by the way, the logs method doesn't work very well.

Answer 44

damn would it be A=prt+p?

Answer 45

Wait a minute...there's a future value formula for simple interest.

Answer 46

The original person who helped you with this used compound interest formula for a simple interest problem.

Answer 47

Big FAIL

Answer 48

The correct formula is

\(FV = PV(1 + rt)\)

Answer 49

\(7,726.99=5,278(1+16r)\)

Answer 50

So it would look like this
7,726.99=5,278(1+r*16)?

Answer 51

i had it backwards. so then we plug in one of the options right

Answer 52

And now I know the correct answer.

Answer 53

I solved for r

Answer 54

That's what you should do

Answer 55

It's easy. You don't have to do logs to figure it out

Answer 56

(1+0.02)16?

Answer 57

@Shorthell, solve for r

Answer 58

Trust me, plugging in isn't always the easy way.

Answer 59

It's a trial and error method at best.

Answer 60

So how would i solve for r?

Answer 61

When you solve for r, you will know what the correct answer is.

Answer 62

First, Divide both sides by 5278
Next, Subtract 1 from both sides
Last, Divide both sides by 16

Answer 63

If you do those steps correctly, you will get the correct answer.

Answer 64

If you don't, you will not get the correct answer .

Answer 65

i got 0.022 rounded

Answer 66

Nope

Answer 67

You did something wrong

Answer 68

Don't ask me what you did wrong because you did not post your steps.

Answer 69

so 7,726.99/5278=1.4638-1=0.4638/16=0.0289 round that and you get 0.029 convert back 2.9%

Answer 70

:D

Answer 71

Thank you!

Answer 72

It's much more satisfying when you solve for r rather than plug and play.

Answer 73

yes yes it is