[PS][interest] HSPA posts

[HSPA]

What annual installment will discharge a debt of 2360 due in four years at 12%PA simple interst?

a) 500
b) 590
c) 874
d) 980

[pankajks2010]

Let the instalment be x:
Now, the first instalment would earn interest for a period of 3 years, similarly the second for 2 years, the third for a year and the fourth would none.
Thus,
x(1.12)^3+x(1.12)^2+x(1.12)+x=2360
Now, solving for x gives approximately 500.

Would be great, if someone could share a quicker method.

Thanks

[vineeshp]

c) 874

Interest per year : 12 %

Total amount due in 4 years : 2360 + 2360 * 4 * 12/100 = 2360 * 148 / 100

Amt each year = 2360 * 148 / 4 * 100

873.2 ~ 874

[vineeshp]

Let the instalment be x:
Now, the first instalment would earn interest for a period of 3 years, similarly the second for 2 years, the third for a year and the fourth would none.
Thus,
x(1.12)^3+x(1.12)^2+x(1.12)+x=2360
Now, solving for x gives approximately 500.

Would be great, if someone could share a quicker method.

Thanks

Dint think of it this way! But again, I am not sure the calc is right.

[HSPA]

OA is pointing 500.. 874 is what I got too..It was not in the original options but I replaced it

Our approach is wrong...

Pankaj has to explain more..

[vineeshp]

Ah! then that method is right. Gotta run now, will work on it again.

[vineeshp]

On second thoughts,

are you telling me that paying 500 for 4 years, that is total of 2000, is enough to discharge a debt of 2360 plus interest for 4 years? That doesnt work!

[pankajks2010]

@Vineeshp: Money makes money by earning interest..So, its not as simple as 500*4=2000
To elaborate: if you make me a payment of 500 at the end of first year..I'll invest that somewhere for 3 years to earn interest..similarly, your second instalment & third instalments would also earn interest..but, not the fourth, because as & when you pay that your term gets over.

@HSPA: Pankaj is explaining more

Now, lets get specific to the question:
Lets assume that the instalment amount is X.
Now, as per the question, one has to pay 4 instalments. The loan gets over as & when you pay the fourth one.
-----after 1 year you pay X-----2nd year you paid X-----3rd year your paid X----fourth year, paid X

and the total of all these payments frees you from the debt

Now, the first instalment that you paid, would earn interest for a period of 3 years (in an ideal world that is what happens, that is how, the whole banking system makes money, although they do a hell lot of other things as well and land us into recession )

Similarly, your second & third instalments would earn interests for the lender. the fourth won't earn any interest.

Which, in mathematical term simplifies to:
x(1.12)^3+x(1.12)^2+x(1.12)+x=2360

Now, its a pain to simplify for x in this equation. That's why I am hoping for the experts to discuss some less calculation intensive method.

[pankajks2010]

Big big mistake: It was actually a question of commonsense.

No calculation required at all...well, the debt to be paid is 2360.

Now, options b,c & d get automatically cancelled. Why because, if these options are multiplied by 4, the total amount paid back would be >=2360. Thus, these can never be the instalment amount as there is interest as well to be considered..

[manpsingh87]

@HSPA: Pankaj is explaining more

Now, lets get specific to the question:
Lets assume that the instalment amount is X.
Now, as per the question, one has to pay 4 instalments. The loan gets over as & when you pay the fourth one.
-----after 1 year you pay X-----2nd year you paid X-----3rd year your paid X----fourth year, paid X

and the total of all these payments frees you from the debt

Now, the first instalment that you paid, would earn interest for a period of 3 years (in an ideal world that is what happens, that is how, the whole banking system makes money, although they do a hell lot of other things as well and land us into recession )

Similarly, your second & third instalments would earn interests for the lender. the fourth won't earn any interest.

therefore after the end of 1st year amount paid would be x+ simple interest of 3 year@12% p.a.= x+(x*12*3)/100=1.36x
similarly for second year it would be 1.24x and for third year it would be 1.12x and for last year it would be x
therefore we have 1.36x+1.24x+1.12x+x=2360
4.72x=2360;
x=500;


PS: pankaj your concept was right but application was wrong...!!!

[pankajks2010]

On second thoughts,

are you telling me that paying 500 for 4 years, that is total of 2000, is enough to discharge a debt of 2360 plus interest for 4 years? That doesnt work!

Dude, because of your above post, I realized that we don't even need to make any equation to solve this question. Big thanks Vineeshp!!

@Manp: Yes, I agree that I employed CI whereas the question explicitly mentions SI. Thanks!!