## murrcat 2 years ago Alex purchased a bedroom set for \$2,276 using a six-month deferred payment plan with an interest rate of 23.49%. What is the balance after the deferment period if payments of \$112 are made each month? \$1,604.00 \$1,884.74 \$2,276.00 \$2,556.74

1. jim_thompson5910

Hint: use A = P(1+r/n)^(n*t)

2. jim_thompson5910

another hint: the monthly payment figure they mention has no affect on the answer (it's put in there to throw you off)

3. murrcat

I know it's not \$2556.74

4. murrcat

or C

5. jim_thompson5910

why not?

6. jim_thompson5910

A = P(1+r/n)^(n*t) A = 2276(1+0.2349/12)^(12*0.5) A = 2556.74

7. murrcat

Then I use the same formula as in the other question?

8. jim_thompson5910

no you're done

9. jim_thompson5910

that's the balance after 6 months

10. jim_thompson5910

so you were second-guessing yourself

11. murrcat

12. jim_thompson5910

it says 2556.74 is wrong?

13. murrcat

Yeah

14. jim_thompson5910

oooh let me try this

15. jim_thompson5910

oh wait nvm

16. jim_thompson5910

does it say which period after the deferment period ends?

17. jim_thompson5910

like "2 months after the deferment period"?

18. murrcat

Nope

19. jim_thompson5910

well the balance at the 6 month mark is 2556.74 if no payments are made during that 6 month window

20. jim_thompson5910

21. murrcat

What is the balance after the deferment period if payments of \$112 are made each month?

22. murrcat

I think it's \$1884.74 because if you multipy 112 by 6 months you get that answer

23. jim_thompson5910

one sec

24. murrcat

ok

25. jim_thompson5910

hmm not sure why, but the closest I'm getting is 1850.99, but that's nowhere near \$1884.74

26. jim_thompson5910

I wonder if it's implying that the interest is added after the payment is made

27. murrcat

Not so sure, I'll just go with \$1,884.74

28. murrcat

Sakura purchased ski equipment for \$1,248 using a six-month deferred payment plan. The interest rate after the introductory period is 23.79%. A down payment of \$175 is required as well as a minimum monthly payment of \$95. What is the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period? A. \$1,112.13 B. \$637.13 Do you know which this one would be? I got \$637.13 but i'm not to sure

29. jim_thompson5910

the down payment of 175 means only 1248-175 = 1,073 is financed

30. jim_thompson5910

one sec

31. jim_thompson5910

so that's the only two choices?

32. murrcat

No there were two more but those were wrong

33. jim_thompson5910

ok nvm that then

34. jim_thompson5910

I'm guessing the interest rate for the introductory period is not given or is it 0%?

35. murrcat

Not given

36. jim_thompson5910

hmm this is a tough one because you can choose not to pay during the deferment period (which I'm assuming is also the introductory period) but I'm trying various scenarios out and I'm not getting anything close I wish they would spell the process out clearer is there an example from the lesson we could use?

37. jim_thompson5910

if so please post it thanks

38. murrcat

No I looked through the lesson and everything was pretty crappy just like all these questions being given from this pretest

39. jim_thompson5910

hmm makes me wish I could read your book/lesson alongside you I'm ok at finance, but stuff like this is making me think otherwise lol

40. murrcat

hmmm

41. murrcat

would you know how to do this one?

42. murrcat

Elliot is graduating from college in six months, but he will need a loan in the amount of \$4,850 for his last semester. He may either receive an unsubsidized Stafford Loan with an interest rate of 6.8%, compounded monthly, or his parents may get a PLUS Loan with an interest rate of 7.8%, compounded monthly. The Stafford Loan has a grace period of six months from the time of graduation. Which loan will have a higher balance and by how much at the time of repayment? The PLUS Loan has a higher balance by \$51.84. The Stafford Loan has a higher balance by \$327.01. The Stafford Loan has a higher balance by \$148.03. The PLUS Loan has a higher balance by \$259.64.

43. murrcat

I'll show you what i did first

44. murrcat

Stafford Loan F = 4850*(1 + 0.068/12)^6 = 5017.25 PLUS Loan F = 4850*(1 + 0.078/12)^6 = 5042.25 Difference PL - SL = 5042.25 - 5017.25 = 28 but 28 isn't in any of the options

45. murrcat

F = L(1 + r/n)^nt F = Future Value L = Initial Loan r = Interest Rate in Decimal Form n = Number of Compounding Periods Per Year (intra-annual) t = Number of Years Loaned

46. jim_thompson5910

ok let me try it out

47. jim_thompson5910

Stafford Loan F = P(1+r/n)^(n*t) = 4850*(1 + 0.068/12)^(12*12/12) = 5,190.28 PLUS Loan F = P(1+r/n)^(n*t) = 4850*(1 + 0.078/12)^(12*6/12) = 5,042.25 Difference 5,190.28 - 5,042.25 = 148.03

48. jim_thompson5910

you forgot to do n*t in the exponent you just did t in the exponent

49. murrcat

oooooooh

50. jim_thompson5910

also, t is in years, so 6 months = 6/12 years 1 year = 12/12 months

51. murrcat

Alright, thanks so much!

52. jim_thompson5910

so The Stafford Loan has a higher balance by \$148.03. yw

53. murrcat

Theres one more question I need help with, or are you annoyed of this?

54. jim_thompson5910

if i don't understand it, i get a bit frustrated lol but it's all in the learning process

55. jim_thompson5910

that last one wasn't so bad since it was definitely more straight-forward

56. jim_thompson5910

I wish I knew how to solve that second to last one though, which is why I wanted to see how the lesson would do it (to see an example)

57. murrcat

Shanelle purchased a dining room set for \$2,620 using a 12-month deferred payment plan with an interest rate of 19.49%. 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? \$2,620.00 \$3,864.00 \$5,796.00 \$3,178.82

58. murrcat

I think this is kinda like the question we could not figure out

59. jim_thompson5910

a bit but this one is more clear though, it says "She did not make any payments during the deferment period"

60. jim_thompson5910

A = P(1+r/n)^(n*t) A = 2620(1+0.1949/12)^(12*1) A = 3178.82 note: this is NOT the answer and a lot of people think it is (which is why this trap is thrown in here). This value is used to find the final answer.

61. jim_thompson5910

3178.82 is the balance after the 12 month deferment period let's use this to find the monthly payment Use the formula P = L((r/n)*(1 + r/n)^(n*t))/((1 + r/n)^(n*t) - 1) where, P = monthly payment L = total amount loaned or amortized r = annual interest rate (APR) n = number of times interest is compounded per year (compounding frequency) t = time in years In this case, P = unknown (we're solving for this) L = 3178.82 r = 0.1949 (19.49% = 19.49/100 = 0.1949) n = 12 t = 2 P = L((r/n)*(1 + r/n)^(n*t))/((1 + r/n)^(n*t) - 1) P = 3178.82((0.1949/12)*(1 + 0.1949/12)^(12*2))/((1 + 0.1949/12)^(12*2) - 1) P = 160.99771204627 P = 161 So we know Payment per period: P = \$161 Number of periods: n*t = 12*2 = 24 Total Amount Paid = (Payment per period)*(Number of periods) = (\$161)*(24) = \$3864 Total Cost is \$3864.00

62. murrcat

Thank you so much! I submitted it now and the Sakura one was 637.13

63. jim_thompson5910

thanks, I'll have to go back over that and think how they got that

64. jim_thompson5910

oh what was the answer to "Alex purchased a bedroom set for..." I don't think we got that either...hmm

65. murrcat

It was \$1,884.74

66. jim_thompson5910

Ok I figured it out. Here's how it works. The rules are that if you pay off the entire balance (this is a big IF), then NO interest will apply. So if you manage to pay off the entire balance of \$2,276 within 6 months (the deferred interest period), then you will be charged NO interest at all. However, companies know very well that the majority of the people will not be able to pay off the entire balance within 6 months. So this is when they retroactively charge interest to make a lot of money. So Alex could have made payments to fully pay off the \$2,276 debt within 6 months...BUT...Alex made payments of \$112 for 6 months, which means he really only paid 6*112 = 672 dollars toward the balance and he's nowhere close to paying off the entire balance of \$2,276 So here's what happens a) Alex did make 6 payments of \$112 or \$672 total over 6 months. So subtract this from the initial balance to get: 2,276 - 672 = 1604. Notice how the balance is not \$0. So the balance was not paid for in full. If it was \$0, then Alex can walk away without having to make any more payments. It's not \$0, so we move onto b) b) Because the balance was NOT paid in full by the end of the 6 month deferment period, this means that interest is applied for every month in the 6 month deferment period. All of this is applied to the initial balance and payments are not factored in (yet). So, P*(1+r/n)^(n*t) = 2276*(1+0.2349/12)^(12*6/12) = 2,556.74 c) The balance is now 2,556.74 dollars. This would be the final answer if Alex did not make any payments at all during this 6 month period. However, alex did make monthly payments of \$112 and he paid the company \$672 so far. So that is subtracted from the balance to get 2,556.74 - 672 = 1,884.74 So that explains why the remaining balance after the 6 month deferment period is \$1,884.74 The same basic steps are applied to the problem with Sakura as well.

67. murrcat

Yeah, that's what I did

68. murrcat

For the Alex one

69. jim_thompson5910

ok great, glad you figured it out

70. murrcat

Hey sorry to bother you but theres a question just like the Alex one Farrah installed a new pool for \$14,730 using a 12-month deferred payment plan with an interest rate of 19.33%. What is the balance after the deferment period if payments of \$527 are made each month? \$14,370.00 \$17,843.62 \$8,046.00 \$11,519.62 My brother tried to do this with me and he got \$8046.00 whereas I got \$11,519.62 I did exactly what you said for the Alex question like 14730(1+0.1933/12)^(12*12/12) = 17843.62 THEN I took 527*12months and got 6324 Subtracted 17843.62 - 6324 = 11519.62 I'm pretty confident with my answer but my brother is telling me I'm wrong?

71. jim_thompson5910

your brother would be right if the interest wasn't applied retroactively, but it is

72. jim_thompson5910

73. jim_thompson5910

it would be nice if it was as simple as saying initial balance - (# of months)*(payment per month) 14730-12*527 8,406 but it's not that simple and that trap is thrown in there to catch students off guard

74. murrcat

Ah okay, thanks :) again!

75. jim_thompson5910

yw

76. murrcat

Garrett is graduating from college in twelve months, but he will need a loan in the amount of \$6,785 for his last two semesters. He may either receive an unsubsidized Stafford Loan with an interest rate of 6.8%, compounded monthly, or his parents may get a PLUS Loan with an interest rate of 7.8%, compounded monthly. The Stafford Loan has a grace period of six months from the time of graduation. Which loan will have a higher balance at the time of repayment and by how much? The PLUS Loan has a higher balance by \$72.54. The PLUS Loan has a higher balance by \$112.83. The Stafford Loan has a higher balance by \$177.86. The Stafford Loan has a higher balance by \$250.40 Is C the right answer?

77. jim_thompson5910

Stafford Loan A = P(1+r/n)^(n*t) A = 6785(1+0.068/12)^(12*1.5) A = 7511.43390604005 A = 7511.43 ------------------------------- PLUS Loan A = P(1+r/n)^(n*t) A = 6785(1+0.078/12)^(12*1) A = 7333.56596333002 A = 7333.57 ------------------------------- The Stafford Loan has the higher balance Difference: 7511.43 - 7333.57 = 177.86 So C is definitely the correct answer

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