Question

Kareem owes $5,127 on a credit card with a 15.9% interest rate compounded monthly. What is the monthly payment he should make in order to pay off this debt in 12 months, assuming he does not charge any more purchases with the card?

$79.94

$427.25

$464.93

$982.42

Answer 1

Annuities? :D

Answer 2

That's one nasty interest-rate... either unrealistic or just plain evil :P
@LuluScavino Are you still here?

Answer 3

yes

Answer 4

So, the annuity involves a fixed monthly payment, let's call that x, paid over 12 months, with its rate of interest being 15.9% compounded monthly...

And we want its present value to be 5127...

Answer 5

okay so what do i do

Answer 6

Well, if the interest rate is 15.9% *compounded monthly*
How much is the effective rate of interest per month?

Answer 7

im so confused sorry?

Answer 8

15.9% annual interest *compounded monthly*
That means... how much is the interest per month?

Answer 9

1.325

Answer 10

That's right. Don't forget the % sign.
So, the annuity formula goes...
\[\Large a_{\bar{n|}}=\frac{1-(1+r)^{-n}}{r}\]
Where r is the effective rate of interest per period...

Answer 11

Now the present value is given by...
\[\Large x\cdot a_{\bar{n|}}\]
And this should be equal to 5127.
Can you now solve for x?

Answer 12

5127(a)

Answer 13

No... 5127 is the present value
and
5127 = ax

Anyway, you'd do well to solve the annuity first.. what is a?
Remember, your r is 1.325%

Answer 14

oh .....

Answer 15

a is not your answer okay?
But it will lead you to it almost instantly.
Now, solve for a...

Answer 16

\[\Large a_{\bar{n|}}=\frac{1-(1+r)^{-n}}{r}\]

But specifically, solve
\[\Large a_{\bar{12|}}\]

Answer 17

but im confused on the formula how does it all come together?

Answer 18

Patience.
First, I want you to solve for \(\Large a_{12}\)...

Answer 19

im so sorry i honestly need to do this quicker because i have lots of questions to answer and this is confusing more than before

Answer 20

i really appreciate you for your help but can you help me quicker please please

Answer 21

Well, it is rather quick, just key it into the calculator...
\[\Large a_{\bar{12|}}=\frac{1-(1+r)^{-12}}{r}\]
we have n = 12, because 12 months will pass...
now, just key it in the calculator, and tell me what you get for \(\Large a_{12}\)

Answer 22

i dont where to find that on my calc

Answer 23

im so so sorry u must hate me

Answer 24

Where to find what?

Answer 25

It's just addition, subtraction, division, an exponent... what can't you find? lol

Answer 26

okay hold on

Answer 27

2

Answer 28

I'm sorry, what?

Answer 29

Idk it

Answer 30

\[\Large a_{\bar{12|}}=\frac{1-(1+\color{red}r)^{-12}}{\color{red}r}\]
What is r?

Answer 31

1.325%

Answer 32

or, in decimal form?

Answer 33

0.1325

Answer 34

no...
0.01325
So now you have the value of r...
now I trust you'll no longer have any difficulty solving
\[\Large a_{\bar{12|}}=\frac{1-(1+r)^{-12}}{r}\]?

Answer 35

okay hold on

Answer 36

63.4

Answer 37

@terenzreignz

Answer 38

nope :)

Answer 39

so then?

Answer 40

is the answer c?

Answer 41

I don't know, let's find out :)

Answer 42

And to find out, it is absolutely crucial for you to find \(a_{12}\)

Answer 43

how?

Answer 44

By following this formula...

Answer 45

\[\Large a_{\bar{12|}}=\frac{1-(1+r)^{-12}}{r}\]

Answer 46

Here, I'll even replace r immediately...
\[\Large a_{\bar{12|}}=\frac{1-(1+0.01325)^{-12}}{0.01325}\]

Answer 47

It really is just a matter of keying it into the calculator (correctly!)

Answer 48

2.5

Answer 49

Not even close, @LuluScavino
Are you guessing? lol... naughty naughty...

Answer 50

no thats what i got

Answer 51

Well, it's not right, so you must have made an error in typing into the calculator...

Answer 52

okay so then what would it be please please please help me get this

Answer 53

I'm trying :)
But you have to help me help you ^_^

You'd be in a rather sorry shape if you can't key this
\[\Large a_{\bar{12|}}=\frac{1-(1+0.01325)^{-12}}{0.01325}\]
correctly into your calculator ...

So please, try again, and be extra careful...

Answer 54

140

Answer 55

The problem with this calculator shenanigan is that I can't see where you made your error... and on top of that, we might not even be using the same kind of calculator :)

and no, 140 is not correct...

Answer 56

then can you please just say it

Answer 57

That's like saying the answer...an act heavily discouraged :)
Besides, I have faith in you ^_^

Answer 58

but ive tried everything and idk what to do?

Answer 59

please i beg u are the last question i have

Answer 60

No you haven't... because... you haven't tried doing it correctly yet :)
Don't give up so easily...

Answer 61

What calculator are you using, btw?

Answer 62

casio

Answer 63

model...?

Answer 64

fx 300 ms

Answer 65

two way power

Answer 66

Then I suggest you do it one at a time... work out the numerator first...
\[\Large a_{\bar{12|}}=\frac{\color{blue}{1-(1+0.01325)^{-12}}}{0.01325}\]
And when it's done, just divide everything by 0.01325

Answer 67

please tell me its -63.444

Answer 68

Impossible.. numerator must be positive...

Answer 69

ok ive tried enough

Answer 70

SERIOUSLY

Answer 71

11.02

Answer 72

ohh... finally :)

Answer 73

Okay so we have \(\Large a_{12}=11.02\)
And \[\Large x \cdot a_{12}=5127\]
Now it's just a simple matter of solving for x

Answer 74

okay hold up

Answer 75

i was rights its C

Answer 76

Yeah... but I suspected you were guessing... so I put you up to it first :)

Answer 77

well look who proved u wrong

Answer 78

Thanks for all the torture :) lol

Answer 79

You didn't...
If you weren't guessing, you wouldn't have had any difficulty whatsoever with \(\Large a_{12}\)
Prove me wrong next time :P
... If I'm ever wrong >:D

Answer 80

Lol (: so then i can ask more questions tmw

Answer 81

We shall see... It's the weekend after all, and let's face it, who studies during weekends?

Answer 82

me

Answer 83

Then you're not spending your weekends correctly :P

Answer 84

adios