What annual payment will discharge a debt of Rs. 580 due in 5 years, the rate being 8 % per SI annum?

[Saumyojit]

What annual payment will discharge a debt of Rs. 580 due in 5 years, the rate being 8 % per SI annum?

Let installment = x

So after 1st year, we have paid installment of Rs. x so he will get an interest on this for that individual year
Si for 1st year on 'x' = (x*8*1)/100 = 8x/100
Si for 2nd year =(x*8*1)/100 =8x/100

I have taken time =1 year in each case as we are considering that individual year interest only.
.
..
...
SO there will be 4 interest all total and 5 installment of x

1:How will i know 580 is principal or amount ?

2; I know that bank is receiving payments. okay tell me one thing when i am paying interest to the bank with the fixed rate. What happens actually .The bank takes the fixd rate at the end of 1st year along with interest or not?? Or the interest gets collected at the end of 4 th year

2: Is my approach wrong?

 

[Deleted member 4993]

Let installment = x

So after 1st year, we have paid installment of Rs. x so he will get an interest on this for that individual year
Si for 1st year on 'x' = (x*8*1)/100 = 8x/100
Si for 2nd year =(x*8*1)/100 =8x/100

I have taken time =1 year in each case as we are considering that individual year interest only.
.
..
...
SO there will be 4 interest all total and 5 installment of x

1:How will i know 580 is principal or amount ?

2; I know that bank is receiving payments. okay tell me one thing when i am paying interest to the bank with the fixed rate. What happens actually .The bank takes the fixd rate at the end of 1st year along with interest or not?? Or the interest gets collected at the end of 4 th year

2: Is my approach wrong?

You have posted the problem statement in the subject line of the post. Like me whole lot of people will miss it.

The bank takes the fixd rate at the end of 1st year along with interest or not?? - in general yes - the bank calculates interest for every period. You need to talk to your teacher (or consult class-notes) to get more definite answer.

The period of interest will be decided - depending on the wording of the problem.

Do you know the formula for calculating annuity or mortgage?

 

[Saumyojit]

Si for 1st year on 'x' = (x*8*1)/100 = 8x/100
Si for 2nd year =(x*8*1)/100 =8x/100

I have taken time =1 year in each case as we are considering that individual year interest only.
.
..
...
SO there will be 4 interest all total and 5 installment of x

this was my approach . BUt i think it is wrong.
MY teacher cannot explain it to me how to solve this .
I dont mug up formulas so no

 

[Deleted member 4993]

Si for 1st year on 'x' = (x*8*1)/100 = 8x/100
Si for 2nd year =(x*8*1)/100 =8x/100

I have taken time =1 year in each case as we are considering that individual year interest only.
.
..
...
SO there will be 4 interest all total and 5 installment of x

this was my approach . BUt i think it is wrong.
MY teacher cannot explain it to me how to solve this .
I dont mug up formulas so no

I am not talking about "cramming" formula. Question is - have you been shown derivation of it - then you could have used the same process here.

Suppose you had decided to pay it all up at the end of 4th year (instead of paying in installments)? How much would be your pay-off? You are going to use this number for your installment calculation.

 

[Saumyojit]

I am not talking about "cramming" formula. Question is have been shown derivation of it - then you could have used the same process here.

Suppose you had decided to pay it all up at the end of 4th year (instead of paying in installments)? How much would be your pay-off? You are going to use this number for your installment calculation.

Please show me the step breakdown.

 

[Deleted member 4993]

Please show me the step breakdown.

Suppose you had decided to pay it all up - in one payment (lump-sum) at the end of 4th year (instead of paying in installments).

How much would be your pay-off?

Can you calculate the above - using process of compound interest?

 

[Saumyojit]

Suppose you had decided to pay it all up - in one payment (lump-sum) at the end of 4th year (instead of paying in installments).

How much would be your pay-off?

Can you calculate the above - using process of compound interest?

WHy ci when it is mentioned si?

 

[Saumyojit]

I am not talking about "cramming" formula. Question is - have you been shown derivation of it - then you could have used the same process here.

Suppose you had decided to pay it all up at the end of 4th year (instead of paying in installments)? How much would be your pay-off? You are going to use this number for your installment calculation.

I am going to use which number for my installment calculation?

 

[Deleted member 4993]

Let's calculate: (assume payment "x" rs/yr)

After 1 year Balance = 580*(1.08) - x

After 2 years Balance = 580*(1.08)^2 - x * (1.08) - x

After 3 years Balance = 580*(1.08)^3 - x * (1.08)^2 - x * 1.08 - x

After 4 years Balance = 580*(1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x

After 5 years Balance = 580*(1.08)^5 - x * (1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x = 0

Now solve for 'x' (see that term in GP)

This is a "non-mugging" (Indian term fot cramming) procedure.....

Go at it

 

[Saumyojit]

Let's calculate: (assume payment "x" rs/yr)

After 1 year Balance = 580*(1.08) - x

After 2 years Balance = 580*(1.08)^2 - x * (1.08) - x

After 3 years Balance = 580*(1.08)^3 - x * (1.08)^2 - x * 1.08 - x

After 4 years Balance = 580*(1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x

After 5 years Balance = 580*(1.08)^5 - x * (1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x = 0

Now solve for 'x' (see that term in GP)

This is a "non-mugging" (Indian term fot cramming) procedure.....

Go at it

WHat did u do?

First of all 580 is p or amt how will i know?

After 1 year Balance should be this 580-[x +(x*8*1)/100]=580- 108x/100
not this 580*(1.08) - x

 

[Saumyojit]

WHat did u do?

First of all 580 is p or amt how will i know?

After 1 year Balance should be this 580-[x +(x*8*1)/100]=580- 108x/100
not this 580*(1.08) - x

Reply .
I want some better answer and clearing of doubt!!!

 

[Dr.Peterson]

Let's calculate: (assume payment "x" rs/yr)

After 1 year Balance = 580*(1.08) - x
After 2 years Balance = 580*(1.08)^2 - x * (1.08) - x
After 3 years Balance = 580*(1.08)^3 - x * (1.08)^2 - x * 1.08 - x
After 4 years Balance = 580*(1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x
After 5 years Balance = 580*(1.08)^5 - x * (1.08)^4 - x * (1.08)^3 - x * 1.08^2 - x*1.08 - x = 0

Now solve for 'x' (see that term in GP)

WHat did u do?

First of all 580 is p or amt how will i know?

After 1 year Balance should be this 580-[x +(x*8*1)/100]=580- 108x/100
not this 580*(1.08) - x

I don't work with financial problems, in part because the terminology of banking doesn't always fit what I know. But I'll say what I think, and you can tell us what you have learned that is different. You said earlier, "My teacher cannot explain it to me how to solve this," but it isn't clear why. (Does the teacher not know the subject, or are you just not understanding what he says?)

Your attempt at the balance after one year, 580 - 108x/100, supposes that you calculate interest on your payment, rather than on the loan. The interest for the first year is not 8% of the payment, x, but 8% of the initial balance, 580. Furthermore, interest does not add to the payment (and therefore subtract from the balance), but rather adds to the balance.

So rather than subtracting 108% of x, you need to add 8% of 580, and subtract x: 580 + 0.08*580 - x = 580(1.08) - x, as SK said.

Does that help? If you think this is wrong, explain why; if you think it is right, do the calculation for the second year, as you understand it.

 

[Saumyojit]

First of all decide 580 is principal that i would have paid if i did not accept installemnt or will be paying at the end of 5 years including interest?

 

[Dr.Peterson]

That's where I can't be sure. The others are clearly assuming this is a loan, as if you borrowed 580 now. The wording is not clear to me.

What have you been taught about this wording? Is the wording you gave exactly what you were asked, or have you translated or paraphrased it?

 

[Saumyojit]

That's where I can't be sure. The others are clearly assuming this is a loan, as if you borrowed 580 now. The wording is not clear to me.

What have you been taught about this wording? Is the wording you gave exactly what you were asked, or have you translated or paraphrased it?

What annual installment will discharge a debt of Rs. 580 due in 5 years at 8% simple interest?

Answer (1 of 2): Most of students always remain confused in these questions so let’s understand the concept. Here total amount (debt) which you have to pay someone is Rs. 580. Now you have the time - 5 years. So now there are many possible ways to pay this :- 1. You can pay him Rs. 580 in the...

www.quora.com

see this'

 

[Saumyojit]

That's where I can't be sure. The others are clearly assuming this is a loan, as if you borrowed 580 now. The wording is not clear to me.

What have you been taught about this wording? Is the wording you gave exactly what you were asked, or have you translated or paraphrased it?

@Dr.Peterson please see the link

 

[Dr.Peterson]

I'm waiting for someone who knows financial terminology to help. You haven't answered the questions I asked; but the answer in the link takes the 580 as a future value, which probably makes sense. (Is there a reason you are dissatisfied with that answer?)

This is not my field, again, so don't depend on me to help. I don't have any magic.

 

[Saumyojit]

I'm waiting for someone who knows financial terminology to help. You haven't answered the questions I asked; but the answer in the link takes the 580 as a future value, which probably makes sense. (Is there a reason you are dissatisfied with that answer?)

This is not my field, again, so don't depend on me to help. I don't have any magic.

now one has explained to me traditional method shown at that link.

 

[Dr.Peterson]

I think it's reasonably clear, if you know anything about interest and algebra. I don't think you've told us what you have learned, to give us a basis for knowing how to help -- if you had started by just quoting the answer and telling us what parts you don't understand, we could have saved a lot of time.

Here is what that person said:

Let installment = x​

So after 1st year, we have paid installment of Rs. x so he will get an interest on this for next 4 years. Similarly , we have paid another installment of Rs. x at the end of years, so he will get an interest on this for next 3 years and so on.​

So (x + x*8*4/100) + (x + x*8*3/100) +(x + x*8*2/100) +(x + x*8*1/100) +(x ) = 580​

or 5x + x*8(1+2+3+4)/100 = 580​

or 5x + 80x/100 = 580​

or 5.8x = 580​

or x = Rs. 100​

So annual installment will be Rs. 100​

The idea is that, with this method of payment, rather than keeping track of the balance, you just imagine the lender putting the money he receives in the bank so that it earns interest until the end, but at simple interest.

The first payment of x is made after 1 year, so it earns 4 years of interest until the end of the 5 years. The lender at the end gets x + x*8*4/100, that is, the principal x plus 8% of x times 4 years. I would have written this as x + 4*0.08x, or as x(1 + 4*0.08).

The second payment of x is made after 2 years, so it earns 3 years of interest, giving the lender x + x*8*3/100.

And so on. The total, (x + x*8*4/100) + (x + x*8*3/100) +(x + x*8*2/100) +(x + x*8*1/100) +(x ), has to equal 580, so you write an equation and solve for x. If you know a little algebra, this should be easy; but let us know if you struggle with the algebra.

Actually, the second "shortcut method" is trickier to understand, because it is explained badly. I was confused by reading that first and getting a wrong idea of how the payment method works. It supposes that each payment is 100, finds how much the lender would get after 5 years, and just scales it up. (This can be done because of the simple interest.) What is there called "first year" really relates to the last payment, which earns no interest. Then it works backward toward the first payment, which earns 4 years of interest.

The "formula method" just applies the same approach to a general problem with variables, using a formula for the sum of an arithmetic progression.

 

[Saumyojit]

So after 1st year, we have paid installment of Rs. x so he will get an interest on this for that individual year
Si for 1st year on 'x' = (x*8*1)/100 = 8x/100
Si for 2nd year =(x*8*1)/100 =8x/100
Si for 3rd year =(x*8*1)/100 =8x/100
like this for 5 terms= (5 * 8x)/100 + each year installment 5x
5x+ (5 * 8x)/100 = 580


I have taken time =1 year in each case as we are considering that individual year interest only.
Is my approach wrong?