Exam problem I failed

[ThomasPaine1]

I spent over an hour of my exam on this multiple-choice problem and I didn't figure it out...can someone solve it for me I can't sleep because of it

On January 1, you contract a debt that must be repaid using seven monthly installments according to the diagram presented below. If you take the option of paying off the debt by making a single payment on April 1 (1/4), what would it be worth if the interest rate is 24%, capitalized monthly?



My results from trying are:
Initial debt 1/1 = 1653.21
Debt on 1/2 = 1486.27
Debt on 1/3 = 1315
April single payment has to be = (Mars debt 1315)*(interest 1.02) = 1341.3
I built an amortization table but 1341.3 is incorrect because it's not one of the answers to the multiple-choice question

n	debt	amort.	interest	payment	month
0	1653.21			0	1/1
1	1486.27	166.94	33.06	200	1/2
2	1315.00	170.27	29.73	200	1/3
3	1142.32	173.68	26.32	200	1/4
4	865.17	277.15	22.85	300	1/5
5	582.47	282.70	17.30	300	1/6
6	294.12	288.35	11.65	300	1/7
7	0	294.12	5.88	300	1/8

All the multiple-choice answers were above 1700$

 

[jonah2.0]

Beer soaked opinion and ramblings follows.

My results from trying are:
Initial debt 1/1 = 1653.21
Debt on 1/2 = 1486.27
Debt on 1/3 = 1315
April single payment has to be = (Mars debt 1315)*(interest 1.02) = 1341.3

I built an amortization table but 1341.3 is incorrect because it's not one of the answers to the multiple-choice question ... All the multiple-choice answers were above 1700$

Minor oversight.
You were extremely close.
Accordingly,
[imath]A=200\frac{1-(1.02)^{-3}}{.02}+300\frac{1-(1.02)^{-4}}{.02}(1.02)^{-3}=[/imath] 1,653.208994 or 1,653.21
Outstanding balance at the end of March (aka the beginning of April), 1/4 as you put it, should be [imath]\left(A(1.02)^2-200\frac{(1.02)^2-1}{.02}\right)(1.02)[/imath]
Alternatively, this amount is equivalent to 200 + outstanding balance of the remaining future four 300 dollars payments. Symbolically, this is [imath]200 + 300\frac{1-(1.02)^{-4}}{.02}[/imath]

Hopefully, you should be able to sleep now. You shouldn't be loosing sleep over stuff like this. So you lost points over the exam. Big deal. Nothing to worry about. The world still spins. Today is victory over yourself of yesterday.

Can you spot your somewhat minor oversight?

 

[ThomasPaine1]

Hello, thank you very much for your detailed explanation. However, the results are all over 1700$ as I said. Furthermore, my understanding of the question is that they want to replace the 200$ April payment with a single, larger payment that would fully resolve the debt.

A) 1754.40
B) 1789.49
C) 1766.64
D) 1777.24
E) 1825.28

 

[tkhunny]

I think we are masterfully confused. Are these payments DAILY or MONTHLY or both?

We'll need a problem statement that makes sense. So far, we don't have one.

For 2 reasons, I do not believe we are replacing ONLY the "April Payment":
1) Why are there remaining payments after the debt is eliminated?
2) Is there an April Payment? "1/4" could easily mean January 4th.

So, please make up your mind and AT LEAST calculate the proper discount rate. Please demonstrate.

 

[ThomasPaine1]

I think we are masterfully confused. Are these payments DAILY or MONTHLY or both?

We'll need a problem statement that makes sense. So far, we don't have one.

For 2 reasons, I do not believe we are replacing ONLY the "April Payment":
1) Why are there remaining payments after the debt is eliminated?
2) Is there an April Payment? "1/4" could easily mean January 4th.

So, please make up your mind and AT LEAST calculate the proper discount rate. Please demonstrate.

There is if you read the original post:
"On January 1, you contract a debt that must be repaid using seven monthly installments according to the diagram presented below. If you take the option of paying off the debt by making a single payment on April 1 (1/4), what would it be worth if the interest rate is 24%, capitalized monthly?"

It clearly states January 1st is the first payment, and every payment after that is monthly (February 1st, March 1st, etc). The amortization table is built by me to try to solve the problem as you can tell by the error at n=2 where debt is 3115 instead of 3115.9954 (3116). I completed the table as if the payments continue uninterrupted to make sure I wasn't making any mistakes. The question asks how much do you have to pay on April 1 to settle the debt without any further payment. Therefore, on April 1 there will be a larger payment that settles the debt that remains unsettled on April 1.

 

[tkhunny]

The purpose of my response was to invite YOU to participate more effectively in the solution.

You're not going to supply the correct monthly discount factor?

 

[jonah2.0]

Beer soaked opinion follows.

Hello, thank you very much for your detailed explanation. However, the results are all over 1700$ as I said. Furthermore, my understanding of the question is that they want to replace the 200$ April payment with a single, larger payment that would fully resolve the debt.

A) 1754.40
B) 1789.49
C) 1766.64
D) 1777.24
E) 1825.28

That's not what you said.
And they are not "results".
They are choices.
This is what you said.

All the multiple-choice answers were above 1700$

If the details of the problem that you gave at post #1 are correct, then it's clear, at least to me anyway, that none of the options given gave the correct answer.
Take a second look at the attached amortization schedule that I provided.

 

[JayJay]

What if we interpret the question to mean there are no payments in February and March; the debt is discharged by just one payment beginning of April?

 

[jonah2.0]

Beer soaked opinion follows.

What if we interpret the question to mean there are no payments in February and March; the debt is discharged by just one payment beginning of April?

On January 1, you contract a debt that must be repaid using seven monthly installments according to the diagram presented below. If you take the option of paying off the debt by making a single payment on April 1 (1/4), what would it be worth if the interest rate is 24%, capitalized monthly?

Yes!
Beautiful.
The problem did indeed mentioned about making a single payment on April 1.
That would give us option A) with
[imath]200\frac{(1.02)^3-1}{.02} + 300\frac{1-(1.02)^{-4}}{.02}[/imath]

NOTE: When I wrote post #7, post #5 wasn't visible to me. The site server must have been drunk.

 

[ThomasPaine1]

That's the answer, no payments at all except for April which means 1 754.40 $. I don't know what the point of making questions like this are. Just trying to trap people, so frustrating.