Question

Help please! I'd really appreciate it. :)

Earl purchased a living room set for $3,592 using a 12-month deferred payment plan. The interest rate after the introductory period is 21.80%. A down payment of $275 is required as well as a minimum monthly payment of $112. What is the balance after the introductory period if only the minimum payment is made until then?

$4,004.92

$2,839.23

$4,116.92

$2,772.92

Answer 1

@jim_thompson5910 Hi there! Do you think you could possibly help me with this? :)

Answer 2

what do you have so far?

Answer 3

Well, honestly I'm stuck on what formula I should use.

Answer 4

how much money is loaned to Earl

Answer 5

$3,592

Answer 6

no

Answer 7

Do I have to add the down payment to that also?

Answer 8

he makes a down payment

Answer 9

that reduces the amount that is loaned to him

Answer 10

example: if the item is $100 and he makes a $10 down payment, then he has to pay off 100-10 = 90 dollars. So 90 dollars is loaned to him

Answer 11

$3,317 then?

Answer 12

yes

Answer 13

Now do I start to utilize the monthly payments he paid throughout the introductory period (which adds up to $1,344)?

Answer 14

it says "The interest rate after the introductory period is 21.80%"

notice the keyword "after"

Answer 15

so I'm going to assume that the interest rate before the introductory period is 0%

Answer 16

Right -- so we technically don't even have to use the interest rate for this problem?

Answer 17

which essentially means that if he can pay off the $3,317 in its entirety before the interest rate goes up, then he won't pay a penny of interest

Answer 18

yeah so I'm thinking we simply do

3317 - 1344 = 1,973

that's the balance after he's made those 12 payments of $112

Answer 19

Hmm . . . what's the next step then? It seems like that's the number it's asking for, but it's not one of the choices.

Answer 20

yeah somehow interest will be added onto that (since he didn't get to $0 before the introductory period is up)

Answer 21

ok I figured it out

Answer 22

Ok, great!

Answer 23

so if Earl pays off the entire balance before the 12 months are up, then he doesn't pay a penny of interest

Answer 24

however, if he has a nonzero balance by the time the 12 months are up, he's charged interest on the original balance (unfair I know, but that's how it works)

so because 3317-1344 = 1973 is nonzero, he still has a balance which accrues interest.

This means that we take the 3317 and use it as principle and have the interest compound

A = P(1+r/n)^(n*t)
A = 3317 (1+0.2180/12)^(12*1)
A = 4,116.91564539528
A = 4,116.92

So when those 12 months are up, the balance is $4,116.92

If he doesn't make any payments, then the balance sticks to $4,116.92

But he made 12 payments of $112, so we subtract off 12*112 = 1344 to get

4,116.92 - 1,344 = 2,772.92

Answer 25

so you can see why it's a good idea for Earl to pay off all the balance by month 12

Answer 26

Wow! That's actually pretty unfair, it totally negates the whole "0% interest" for the introductory period in this case due to his nonzero amount . . . I feel bad for Earl lol :P

Anyway, thank you so much for breaking it down! I appreciate your assistance to the fullest. :D

Answer 27

yeah it's deferred in a sense that it's saying "we'll put off the interest rate for 12 months IF you can pay off the balance. If not, then we'll go back to day 1 and recompute interest just as if the 0% interest rate never happened"

Answer 28

so on the surface, it looks like a good deal but only if you can pay it all off by 12 months