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

I give up. Go back and read what I've written, then think about it more.

YOU ARE NOT GETTING ANY INTEREST! THEY ARE.
 
Dr.Peterson said:
I give up. Go back and read what I've written, then think about it more.

YOU ARE NOT GETTING ANY INTEREST! THEY ARE.
Click to expand...
okay suppose i am paying a installment of x to the bank at the end of first year then si gaining by the bank calculated will be on that year only?


if uexplain me this line then thesum is over : Each amount paid earns simple interest from then until the end of the 5 years.
 
Saumyojit said:
okay suppose i am paying a installment of x to the bank at the end of first year then si gaining by the bank calculated will be on that year only?

if uexplain me this line then thesum is over : Each amount paid earns simple interest from then until the end of the 5 years.
Click to expand...
This should be clear by now. They have the money from the first payment for four years, so they get 4 years of interest, not just 1.
 
Probably; see post #37.

But we don't need to know. And we don't know for sure, because the problem doesn't tell us anything, as I've pointed out repeatedly (even whether it is a bank at all).
 
Dr.Peterson said:
This should be clear by now. They have the money from the first payment for four years, so they get 4 years of interest, not just 1.
Click to expand...
why will they have the money from 1st payment for 4 years? They can keep the payment as long as they want or can lend the amount to anyone. I have done my part of giving installment.
 
I don't think there's more I can do to help you, if your textbook doesn't teach you anything about how investments work. If your book is only for review for a test, and doesn't teach anything, then find one that does.

But if I were running a bank, I would not put the money people gave me in a vault doing nothing; I would lend it, or buy stock with it, or anything that will earn more money. And when I say "they have it", I mean that they own it, even if they invest it -- just as when you put money in a bank, it is still yours, and you earn the interest.

Presumably the problem is meant to assume some such rational behavior, even if it does not reflect exactly how things work in real life. But if they tell you a bank does this kind of loan (or whatever this is), then they need to explain to you how it works.
 
even if they have it why they get 4 years of interest . THey will get interest on the new scheme to which they are lending to the borrower
 
Dr.Peterson said:
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.
Click to expand...
@Dr.Peterson here u have said that the man will be getting interest. please be clear

even if bank have it , why they get 4 years of interest . THey will get interest on the new scheme to which they are lending to the borrow
 
I have nothing more to say until you can provide some evidence about how this loan works. The problem is not clear enough about such details. Find some source that explains it.
 
Dr.Peterson said:
I have nothing more to say until you can provide some evidence about how this loan works. The problem is not clear enough about such details. Find some source that explains it.
Click to expand...
U are a mathematician u should dig deep and find out the process .
I checked every where but to no avail
 
@Jomo
@Dr.Peterson
@Dr Ahkim
This sum is still hanging .
Check the link
PLEASE EXPLAIN this line : You pay $200. That will have growth of $200 * 0.04 * 3 years = $24 by the end
 
Last edited by a moderator:
Was the original problem written in English or some other language such as Hindi? If it was written in English, please give the original text completely and exactly. If not in English, give your best effort at a translation of the entire exercise.

A comment to Dr. Peterson. The problem does not appear to me to have any relationship with US commercial practice (and I spent 44 years of my life working in banking in the US including 10 years as a bank director). I greatly doubt the problem has much relationship with Indian commercial practice. Thus, technical vocabulary and commercial practice, which vary from country to country, are probably not issues.

It looks to me as though this is a made-up exercise divorced from any actual financial transaction but rather designed to utlize the definition of simple interest and the formula for computing the future value of a sequence of equal payments at compound interest. I cannot be sure of this because the wording of the problem is unclear. Is the 580 due now or in five years? We are not told. I suspect what is meant is that 580 plus simple interest at 8.5% per year is due in five years, but all we are given is only the meaningless phrase "per SI annum." No information is given on the rate appropriate for interest being compounded annually.

Because this student has admitted that he has not "mugged up" any formulas, among which he seems to include definitional formulas, he understandably finds the problem difficult. I find the problem as given impossible because it is insufficiently specified.
 
Subhotosh Khan said:
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
Click to expand...
thanks
 
You must log in or register to reply here.
Top