Say I bought a TV for $289.99. I have a deferment plan. The minimum total purchase to get the plan is $149 and up. I picked the 6 month financing. My APR is 25.24%. And the minimum payment requirment is $25....
So this is my scenerio. can someone help me answer the following questions? @jim_thompson5910

- anonymous

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- jim_thompson5910

what questions are there?

- anonymous

yay! ok hold on a sec :)

- jim_thompson5910

ok

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## More answers

- anonymous

##### 1 Attachment

- jim_thompson5910

ok one sec

- anonymous

ok :))

- jim_thompson5910

I'm curious if you've learned the remaining balance of a loan formula at all?

- anonymous

ummm i think so one sec

- jim_thompson5910

ok

- anonymous

heres a part of the lessons i snipped out. im pretty sure this is it.

##### 1 Attachment

- jim_thompson5910

are there any more formulas? I see one that will help with the monthly payment, but I don't see a remaining balance formula

- anonymous

let me double check

- jim_thompson5910

btw the formula at the very top will be useful for part 2 (since you don't pay down any of the debt, which makes calculating the balance much easier)

- anonymous

no there are no other formulas

- anonymous

here are snapshots of the lesson summary to maybe help?

##### 2 Attachments

- jim_thompson5910

sorry got distracted, one sec

- jim_thompson5910

well I have a remaining balance formula, but it's a bit complicated and I'm not sure you've learned it yet

- anonymous

well lets try it!

- jim_thompson5910

ok the formula is
B = L*(1+r/n)^k - (P*n/r)*( (1+r/n)^k - 1 )
Where,
B = Remaining balance at month k (payment is made on month k)
L = Loan amount
P = Payment per period
r = Annual interest rate
n = Compounding frequency
k = Point in time where you want to find the remaining balance (time in months)

- anonymous

no i havnt learned that but i can see what they all mean

- jim_thompson5910

In this case,
B = Unknown (we're solving for this)
L = 289.99
P = 25
r = 25.24
n = 12 (we're compounding it monthly)
k = 6 (you want to find the remaining balance at month 6)

- jim_thompson5910

Plug all these values in to get
B = L*(1+r/n)^k - (P*n/r)*( (1+r/n)^k - 1 )
B = 289.99*(1+0.2524/12)^6 - (25*12/0.2524)*( (1+0.2524/12)^6 - 1 )
B = 170.453723678253
B = 170.45

- anonymous

this is the remaining balance?

- jim_thompson5910

So what this means is that if you buy a TV that costs 289.99 and you make 6 monthly payments during the deferment period, this will mean that you would still owe $170.45 after the deferment period is over

- jim_thompson5910

6 monthly payments of $25*

- anonymous

this is number 1 right?

- jim_thompson5910

yes

- anonymous

thats easier to understand then i expected actually! haha lets move on to number two

- jim_thompson5910

ok now we use the monthly payment formula
since it says that we don't have to show work, we can use a monthly calculator instead
which method do you want to use?

- anonymous

we can just use the calculator:) its much easier

- jim_thompson5910

ok great, go here then
http://www.bankrate.com/calculators/mortgages/loan-calculator.aspx
and type in 170.45 into the loan amount box, 5 in the years box, and 25.24 in the rate box and hit calculate
tell me what you get

- anonymous

ok one sec :)

- jim_thompson5910

ok

- anonymous

i got 5.03?

- jim_thompson5910

me too

- jim_thompson5910

that's the monthly payment and the answer for #2

- jim_thompson5910

for #3, during the deferment period you paid 25*6 = 150 dollars
then after the deferment period, you paid 60*5.03 = 301.8 dollars (since 5 years = 60 months)
in total you paid 150 + 301.8 = 451.80 dollars
the total cost is therefore 451.80 dollars

- jim_thompson5910

#4 should be pretty straight forward

- anonymous

so 281.35?

- jim_thompson5910

no you subtract 451.80 - 289.99

- jim_thompson5910

this is to find out how much extra you pay over the long run (if you finance instead of just pay all of the $289.99 at once)

- anonymous

161.81? :)

- jim_thompson5910

yep

- anonymous

for the next little section i know im going to have some trouble because thiese questions dont include the minimum payment...

- jim_thompson5910

ok for #1 in the next section, you are going to use the formula that is B = P(1+i)^(nt)

- jim_thompson5910

In this case
P = 289.99
i = 0.2524/12
n = 12
t = 6/12 = 0.5

- anonymous

i didnt get 0.5??

- jim_thompson5910

t is time in years
so 6 months = 6/12 = 0.5 years

- jim_thompson5910

that's why t = 0.5

- anonymous

oh i miscalculated it. now i got it:)

- jim_thompson5910

ok great

- anonymous

ok what do we do for number 2?

- jim_thompson5910

what did you get for #1

- anonymous

.05?

- jim_thompson5910

no that's not the answer to #1

- jim_thompson5910

use the formula I wrote above

- anonymous

170.45

- jim_thompson5910

no that was the answer to #1 from part 1

- anonymous

oh i thought thats what you meant

- jim_thompson5910

no i mean #1 from part 2

- anonymous

i dont know? i dont know how to find the mpnthly pay ment....

- jim_thompson5910

plug these values
P = 289.99
i = 0.2524/12
n = 12
t = 6/12 = 0.5
into the formula below
B = P(1+i)^(nt)

- anonymous

wouldnt that give me the same exact answer since we already plugged these numbers into this formula?

- jim_thompson5910

no it's much higher than 170.45

- anonymous

ok one sec.

- jim_thompson5910

ok

- anonymous

so B= 328.566?

- jim_thompson5910

no

- jim_thompson5910

oh wait, hold on

- anonymous

what? i dont understnad i plugged them all and and solved it...

- jim_thompson5910

sorry made a typo, I'm getting
289.99(1+0.2524/12)^(12*0.5) = 328.565943133299
so you are correct

- jim_thompson5910

so the answer to #1 in part 2 is 328.57

- anonymous

oh whew! and woops i thought this was the answer to number 2 in part 2 lol

- jim_thompson5910

no you use that calculator you used from part 1

- jim_thompson5910

to answer #2 in part 2

- anonymous

oh! let me try this one on my own hold on just a sec :)

- anonymous

oh gosh not even close. i dont know what to plug in

- jim_thompson5910

328.57 in the loan amount box
5 in the years box
25.24 in the rate box

- anonymous

ok one sec

- anonymous

$9.69

- jim_thompson5910

good

- anonymous

yay!

- jim_thompson5910

to answer #3, you need to multiply the number of months (60) by the monthly payment ($9.69) to get the total cost

- anonymous

581.4?

- jim_thompson5910

good

- anonymous

thats the answer to number #3? it seems like we did more work in part 1 number #3? rather than this onw?

- jim_thompson5910

well that's because back in part 1, there's the amount you add on during the deferment period

- jim_thompson5910

but you don't have to worry about that in this part

- anonymous

oh gotcha! that makes sense:)

- anonymous

now number 5 :)

- jim_thompson5910

what did you get for #4

- anonymous

oh my gosh sorry ahah im getting ahead of myself. i meant number 4

- jim_thompson5910

#4 is pretty straight forward, tell me what you get

- anonymous

38.58!

- jim_thompson5910

you are subtracting the original cost from the total cost
581.4-289.99 = ??

- anonymous

291.41

- jim_thompson5910

good

- jim_thompson5910

for the last question #5, you need to divide 289.99 by 6 to get
289.99/6 = 48.3316666666667
then you round that up to the nearest penny to get 48.34
so the monthly payment of $48.34 is guaranteed to pay off the $289.99 bill before interest kicks in

- anonymous

so 48.34?

- jim_thompson5910

yes

- anonymous

i was confused a little bit. i got it now! Can you help me with one more section?

- jim_thompson5910

glad it's making sense and sure

- anonymous

its just the analysis :)

- anonymous

##### 1 Attachment

- jim_thompson5910

ok tell me what you got for this

- anonymous

what do you mean?

- jim_thompson5910

how far did you get with this section

- anonymous

oh im still on number 1

- jim_thompson5910

so any ideas what the difference between the total cost and the original cost represents?

- anonymous

it represents which one is better?

- jim_thompson5910

not quite

- jim_thompson5910

the TV originally costs $289.99
but if you pay more overall ($451.80) when you use the deferment plan, then that difference is the amount of total interest you pay

- anonymous

so it basically represents the total amount you pay for the tv?

- jim_thompson5910

it's the amount extra you pay for delaying the payments and spreading them out more

- jim_thompson5910

so that's what you have to worry about: if you pay less per month or put off payments (ie defer them), then you end up paying more overall

- jim_thompson5910

you could either buy the TV completely and pay $289.99 and this is a one time payment (or could be done within 6 months)
OR
you could spend $451.80 if you pay the min payment of $25 during the deferment period and then pay the monthly payment of $5.03 for the next five years
so you can see that you pay a lot more money for the TV in the long run over the 5 year period

- anonymous

ooooh :) i get it now haha

- jim_thompson5910

yes this is why credit is dangerous and why people get into trouble with it

- anonymous

yikes! and number 2 i say no because i would only have to pay $48.34 a month is i dont pay with the minimum payment

- jim_thompson5910

correct, the min payment is not enough to buy the TV

- jim_thompson5910

that's another thing you have to make sure you don't do: do NOT go for the min payment or you will spend a lot longer paying it off and you'll be spending a lot more money in the long run

- anonymous

exactly:) but i dont know about number 3 :(

- anonymous

@jim_thompson5910

- jim_thompson5910

what was the total cost in part 1?

- anonymous

170.45

- jim_thompson5910

no, the total cost

- anonymous

oh161.81

- anonymous

@jim_thompson5910

- jim_thompson5910

no

- jim_thompson5910

look at #3 in part 1

- anonymous

oh 451.80 dollars!

- jim_thompson5910

yes that's the total cost if you do the min payment during the deferment period

- jim_thompson5910

what is the total cost if you don't do the min payment during the deferment period

- anonymous

581.4?

- jim_thompson5910

now subtract the two figures

- anonymous

129.6?

- anonymous

i think?

- jim_thompson5910

good

- jim_thompson5910

that's the difference between the two plans
so if you don't make the min payments, then you pay 129.60 more dollars

- jim_thompson5910

so you can see why that law is put in place

- anonymous

why?

- jim_thompson5910

because you pay more if you don't make the min payment

- jim_thompson5910

so it's like a way to stop companies from getting away with charging too much for a product

- anonymous

what about number 5?

- anonymous

@jim_thompson5910

- jim_thompson5910

what do you think about #5

- jim_thompson5910

If you're in college, then perhaps you have a college loan
so you may know a thing or two about them

- anonymous

im not in college :( but i think it has something to do with paying off payments during a period of time?

- jim_thompson5910

usually the interest rates for student loans are much lower than deferment plans you find in stores
these interest rates are lower because some loans are subsidized by the government (ie they pay for a portion of it to keep the rates low)

- jim_thompson5910

also there's a lot more competition which is why the rates are lower

- jim_thompson5910

so instead of finding a 25.24% interest rate (which is really high), you'll find interest rates like 3.4% or 6.8%

- anonymous

i dont see what this has to do with them being similar or different? i dont get it

- jim_thompson5910

I just explained how they're different, their rates are different (usually much lower)

- anonymous

oh! because of the rates! i got it now. Thank you so much for helping me with my assignments. I take an online math class so its hard to understand the material but for some reason i understand it after you explain it steo by step!

- jim_thompson5910

glad it's making sense now

- anonymous

thank you so so so soooo much!

- jim_thompson5910

you're very welcome

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