Salina purchased a dining room set for $1,730 using a 12-month deferred payment plan with an interest rate of 23.45%. She did not make any payments during the deferment period. What will the total cost of the dining room set be if she must pay off the dining room set within two years after the deferment period?

Question

anonymous · Answer

@kitty828 Do you know which formula to apply?

anonymous · Answer

I have no idea how to do this problem

anonymous · Answer

I ask about the formula you've learned from your class, not how to solve it!

anonymous · Answer

M=B i(1+i)nt over (1+i)nt-1

B=P(1+i)nt

anonymous · Answer

I'm not sure I couldn't figure that out /: I couldn't figure out the i or the nt either

anonymous · Answer

no ):

anonymous · Answer

yes

anonymous · Answer

As the rule of thumb, 23.45% is annual rate
-> How can you find monthly rate?

anonymous · Answer

I am very confused. these are the options for answers


$2,754.72

 $4,132.08

 $1,730.00

 $2,182.26

anonymous · Answer

No, I guide you to think!
What the relation between year and month?

anonymous · Answer

what?

anonymous · Answer

You probably know how many months per year :)

anonymous · Answer

12

anonymous · Answer

Now, you know 23.45% is the interest rate per year
Could you find interest rate per month = ...?

anonymous · Answer

oh wait

anonymous · Answer

1.9

anonymous · Answer

Pretty close, except you forget to divide by 100 :)

anonymous · Answer

.0195?

anonymous · Answer

Yup, you're making a progress :)
Can you find the time now ?

anonymous · Answer

the time? how would I do that?

anonymous · Answer

Convert year into months, because the interest based on months :)

anonymous · Answer

so 12?

anonymous · Answer

Check for the period ?

anonymous · Answer

sorry 24. i didnt relize it was 2 years

anonymous · Answer

Sorry I'm on the phone solving some family trouble!

anonymous · Answer

its ok thank you for helping me!

anonymous · Answer

So now you know i and nt, correct!

anonymous · Answer

so this is the correct answer? 
 $4,132.08

anonymous · Answer

Can you plug into the formula:
M  =  B i(1+i)^nt / (1+i)^(nt-1)

anonymous · Answer

yes?

anonymous · Answer

Could you show your calculation?

anonymous · Answer

I don't know i'm so confused at this point. Where do I need to plug that number into on the formula? into i?

anonymous · Answer

1. Balance from 12-month deferred payment plan:
    B  =  P       (1 +  i) ^nt 
        = 1,730 ( 1+ .0195 ) ^ 12 
        = $2,182.26
2. Monthly payment after 12 months:
    M =          B            i     (1  +  i  )   ^nt / (1+i)^ nt  - 1
        = $2,182.26 * .0195 ( 1.0195) ^24 / [ ( 1.0195) ^24 -1 ] 
        = $114.78
3. Total cost: 
     T = 24 * $114.78 = $ 2, 754.72

anonymous · Answer

this answer is correct