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i have a question for my math practice but i do several ways but i still get the wrong answer, please help:

Loan payments of $700 due 3 months ago and $1000 due today are to be paid by a payment of $800 in two months and a final payment in five months. If 9% interest is allowed, and the focal date is five months from now, what is the amount of the final payment.

I calculate by using future value formula: S=P(1+r*t)

The first method i try is:

700(1+.0.09*8/12) + 1000(1+0.09*5/12) + 800(1+0.09*3/12)= 2597.5

2nd attemp:

700(1+0.09*8/12) + 1000(1+0.09*5/12)= 800(1+0.09*3/12) + X

==>X= 961.5

Can Anyone help me? ( this is simple interest)

K Tiger
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3 Answers3

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The focal date is the date of the last payment. At this date, the amount of the debt is $$ FV_1=700\left(1+0.09\times\frac{8}{12}\right)+1000\left(1+0.09\times\frac{5}{12}\right)=1779.5 $$ and the amount of the repayments is $$ FV_2=800\left(1+0.09\times\frac{2}{12}\right)+P=818+P $$ We must have $FV_1=FV_2$ and then $$ P=1779.5-818=961.5 $$

If you use compound interest, then $$ 700\left(1+\frac{0.09}{12}\right)^8+1000\left(1+\frac{0.09}{12}\right)^5=800\left(1+\frac{0.09}{12}\right)^2+P $$ that is $$ P=1781.19-818.14=963.05 $$

alexjo
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I instead would try:

  • \$700 to be paid in 5 months,
  • \$100 to be paid in 2 months,
  • \$900 to be paid in 5 months.

Assuming simple interest (without exponential formulas), a 9% anual, and liquidating first the oldest debt, and carrying the values into the focal date, we shall apply again the interest over every paid amount:

  • 3 months from the first payment into the focal date
  • no months from the second payment into the focal date

Hence the final paid value with the focal date correction should be: $\$700\cdot(1+0.09\cdot5/12)\cdot(1+0.09\cdot3/12)+\$100(1+0.09\cdot2/12)\cdot(1+0.09\cdot3/12)+\$900\cdot(1+0.09\cdot5/12)= \$1780.12$

From here the amount of final payment, at the focal date is: $\$900\cdot(1+0.09\cdot5/12)=\$933.75$

Note that making a payment at the 3rd past month involves a factor of $(1+0.09\cdot 3/12)$. This is the exact amount paid at that instant. Carrying this paid value with a focal date at the 5th next month involves a second factor of $(1+0.09\cdot 5/12)$, so the final paid quantity have a doubled factor of $(1+0.09\cdot 3/12)\cdot(1+0.09\cdot 3/12)$.
Of course, this depend on the system applied.

Brethlosze
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  • I don't really understand, how can you get the $100, $900 and those months? And yes this is simple interest. – K Tiger Oct 01 '17 at 04:25
  • I am considering the oldest debt is paid first. Hence the payment of $800 in next 2 months will cover the $700 from last 3 months, and a partial $100 for the $1000 of today. And the remaining $900 to be paid in the next 5 months. – Brethlosze Oct 01 '17 at 04:28
  • Check the edit, with the correction of the value into the focal date. Because this is simple interest, it is different to apply $700 by 5 periods and then 3 more periods. WIth compound interest, the original amount and their interest are reapplied automatically, and it is the same to write factors for 5 and 3 months than for 8 months. – Brethlosze Oct 01 '17 at 04:40
  • I see your point now. It's quite confused at the first time because i think i can only use the amount of payment to calculate which are 700, 1000 and 800. The only fomula i have until now to calculate this kind of question is S=P(1+r*t) so i was kinda confused with the way you expanded the fomula. – K Tiger Oct 01 '17 at 04:50
  • If the debt is two payments of $700 and $1000, and you pay $800, you have to decide how the debt is going to be paid. You pay part of the $1000 and keep accumulating interest in the $700?. Or you pay the $700 and part of the $1000 with interest from today?. If you have similar examples, we could decide further. – Brethlosze Oct 01 '17 at 15:34
  • I have a preety much the same example and i could do it right. However, this practice is quite something. – K Tiger Oct 01 '17 at 16:40
  • Which is the correct solution, by the way? – Brethlosze Oct 02 '17 at 01:05
  • I don't know yet, because i only have 4 attemps and i already use 3 for this excercise so i have to spend more time to consider these results. – K Tiger Oct 02 '17 at 02:06
  • I insist one of the previous question from your guides will settle this question...... – Brethlosze Oct 02 '17 at 23:30
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    it turns out my second answer is the correct one but i have to put .50 instead of .5. Weird system. – K Tiger Oct 03 '17 at 02:17
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I use the present time as reference date. There are two methods with the corresponding equations:

$\color{blue}{\texttt{a) simple interest}}$

$$700\cdot (1+0.09\cdot 3/12)+1000=\frac{800}{1+0.09\cdot 2/12}+\frac{x}{1+0.09\cdot 5/12}$$

$\Rightarrow x=962.36$

The result is a little bit different from yours due the different reference dates.

$\color{blue}{\texttt{b) compound interest}}$

$$700\cdot (1+0.09/12)^3+1000=\frac{800}{(1+0.09/12)^2}+\frac{x}{(1+0.09/12)^5}$$

$\Rightarrow x=963.05$

callculus42
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  • In fact, the reference date should be the focal day( my teacher told me that), The focal day should be on the far right of the time line(3 month ago---now---next two month---next five month"al so the focal day"). So i think we should also use future value for $800 and X section, which is my 2nd method? Don't you think so? – K Tiger Oct 01 '17 at 16:33
  • @KTiger I have read over that the focal date has to be in 5 months from now. In this case your equation and your result with $X= 961.5$ is right. By the way, if you apply the compound interest method it doesn´t matter which day is the focal day. The equation remains equivalent due equivalent transformations. – callculus42 Oct 01 '17 at 17:48
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    That's the problem, However the system still tells me that i was wrong. There is a sentence in the exercise "round to 2 decimal places", i wonder do i have to make it 961.50 to get a correct result or not. – K Tiger Oct 01 '17 at 17:52
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    @KTiger It depends on how the system works. Mathematically the results are identical, $961.5=961.50$. I would try what you have suggested. – callculus42 Oct 01 '17 at 18:02