Question

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

Answer 1

what questions are there?

Answer 2

yay! ok hold on a sec :)

Answer 3

ok

Answer 4

ok one sec

Answer 5

ok :))

Answer 6

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

Answer 7

ummm i think so one sec

Answer 8

ok

Answer 9

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

Answer 10

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

Answer 11

let me double check

Answer 12

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)

Answer 13

no there are no other formulas

Answer 14

here are snapshots of the lesson summary to maybe help?

Answer 15

sorry got distracted, one sec

Answer 16

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

Answer 17

well lets try it!

Answer 18

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)

Answer 19

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

Answer 20

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)

Answer 21

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

Answer 22

this is the remaining balance?

Answer 23

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

Answer 24

6 monthly payments of $25*

Answer 25

this is number 1 right?

Answer 26

yes

Answer 27

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

Answer 28

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?

Answer 29

we can just use the calculator:) its much easier

Answer 30

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

Answer 31

ok one sec :)

Answer 32

ok

Answer 33

i got 5.03?

Answer 34

me too

Answer 35

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

Answer 36

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

Answer 37

#4 should be pretty straight forward

Answer 38

so 281.35?

Answer 39

no you subtract 451.80 - 289.99

Answer 40

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)

Answer 41

161.81? :)

Answer 42

yep

Answer 43

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

Answer 44

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

Answer 45

In this case

P = 289.99
i = 0.2524/12
n = 12
t = 6/12 = 0.5

Answer 46

i didnt get 0.5??

Answer 47

t is time in years

so 6 months = 6/12 = 0.5 years

Answer 48

that's why t = 0.5

Answer 49

oh i miscalculated it. now i got it:)

Answer 50

ok great

Answer 51

ok what do we do for number 2?

Answer 52

what did you get for #1

Answer 53

.05?

Answer 54

no that's not the answer to #1

Answer 55

use the formula I wrote above

Answer 56

170.45

Answer 57

no that was the answer to #1 from part 1

Answer 58

oh i thought thats what you meant

Answer 59

no i mean #1 from part 2

Answer 60

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

Answer 61

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)

Answer 62

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

Answer 63

no it's much higher than 170.45

Answer 64

ok one sec.

Answer 65

ok

Answer 66

so B= 328.566?

Answer 67

no

Answer 68

oh wait, hold on

Answer 69

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

Answer 70

sorry made a typo, I'm getting

289.99(1+0.2524/12)^(12*0.5) = 328.565943133299

so you are correct

Answer 71

so the answer to #1 in part 2 is 328.57

Answer 72

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

Answer 73

no you use that calculator you used from part 1

Answer 74

to answer #2 in part 2

Answer 75

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

Answer 76

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

Answer 77

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

Answer 78

ok one sec

Answer 79

$9.69

Answer 80

good

Answer 81

yay!

Answer 82

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

Answer 83

581.4?

Answer 84

good

Answer 85

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

Answer 86

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

Answer 87

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

Answer 88

oh gotcha! that makes sense:)

Answer 89

now number 5 :)

Answer 90

what did you get for #4

Answer 91

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

Answer 92

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

Answer 93

38.58!

Answer 94

you are subtracting the original cost from the total cost


581.4-289.99 = ??

Answer 95

291.41