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Saumyojit

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When Interest is compounded anually but time is in fraction (3 2/5 years )...

A=P(1+r/100)^3 *(1+{(2/5)*R}/100 )

HOw did it came ?

I understood the first part P(1+r/100)^3 and after this 2/5 years means more than quaterly. How does the second portion of the formula is being done?
 
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They are doing this as if it were "compound interest" for 3 years, then simple interest for the remaining 2/5 year.

You say "2/5 years means more than quarterly". That is true but irrelevant since the interest is compounded annually not quarterly.
 
How is it possible there are doing simple interest when they are compounding annually?
 
Because the annual "compounding" happens at the end of each year. If there is no full year, there is no compounding.
 
HallsofIvy said:
Because the annual "compounding" happens at the end of each year. If there is no full year, there is no compounding.
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If there is no full year there will be no compounding that doesn't mean I need to implement simple interest here or is it?.


I can't find the logic behind putting simple interest if I can't do compund interest.
Is there any rule laid out by any great mathematician or is there any logic..
 
IF there will be no compounding that doesn't mean I need to implement simple interest here
 
This is not really a question about a mathematical rule, but about what a bank will do in practice. You need to find out what rules they choose to follow.

They could conceivably say that they only apply interest every year, and you get no interest for the time since the last compounding. That would be fair if they disclosed that to you. (But you would not want to use that bank, and you would not leave your money there beyond a whole number of years.)

It seems more reasonable that they would do what has been suggested: calculate and apply interest at the end of each year (which is what annual compounding is), and again when you withdraw your money (which would necessarily be simple interest).

Compound interest merely means simple interest applied periodically, and added into the account so that past interest now earns interest. The last bit of interest just goes directly to the depositor, so it is not compounded.
 
Dr.Peterson said:
It seems more reasonable that they would do what has been suggested: calculate and apply interest at the end of each year (which is what annual compounding is), and again when you withdraw your money (which would necessarily be simple interest).

Compound interest merely means simple interest applied periodically, and added into the account so that past interest now earns interest. The last bit of interest just goes directly to the depositor, so it is not compounded.
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Compound interest merely means simple interest applied periodically. I did not understand these lines .


So that past interest now earns interest.
 
They could conceivably say that they only apply interest every year, and you get no interest for the time since the last compounding.
please explain this line with example . last compunding mens?
 
Saumyojit said:
Compound interest merely means simple interest applied periodically. I did not understand these lines .


So that past interest now earns interest.
Click to expand...

So that past interest now earns interest. I have understood this line .
but the former is still in doubt
 
Saumyojit said:
"Compound interest merely means simple interest applied periodically." I did not understand these lines .

"So that past interest now earns interest."
Click to expand...

(I have inserted quotation marks in what you wrote so that I can tell what you are saying, and what I said. I have often had trouble following what you write for this reason.)

Tell me what compound interest means, as you understand it. How was the concept introduced to you?

If it is compounded annually, then each year they are paying one year's interest on the amount at the start of the year. That is calculated the same way as simple interest. What makes compound interest different is that they then add this interest to the principal, so that for the next year, they calculate interest based on this new total -- they are paying interest not only on the original principal, but also on the interest added in after the first year. It's a common saying: compound interest means you pay (or get) interest on the interest, which is why it grows so much faster than simple interest.

Saumyojit said:
"They could conceivably say that they only apply interest every year, and you get no interest for the time since the last compounding."
please explain this line with example: What "last compounding" means?
Click to expand...

Each time they pay interest and add it in, that can be called compounding. So "the last compounding" means "the last time they paid interest, at the end of the year". That is, they calculate interest for that last 2/5 of a year.
 
in 3 2/5 years there are 4 interests all total.
iF the last compunding means calculation of interest(CI) for the last 2/5 part of the year then how last part is calculated using si ?Then there is no meaning of last compunding .
 
@
Dr.Peterson
there are 4 interests all total in this case.
IF the last compounding means calculation of interest(CI) for the last 2/5 part of the year then how last part is calculated using si ?Then there is no meaning of last compounding , then last compunding means upto 3rd year that has been calculated.
 
What I called the last compounding (and bankers probably have a better term for it), was the end of the third year. I never said there are four "compoundings". But interest is calculated four times. What I said was that the 2/5 year is "the time since the last compounding".

Interest is calculated for the first year, and for the second year, and for the third year, and then for the final 2/5 year. Each of those uses simple interest: the amount at the start, times the interest rate, times the time interval (1 or 2/5).
 
@Dr.Peterson
Each of those uses simple interest . HOw can each of those can be using simple interest . If u see P(1+r/100)^3 this is the formula of compound interest which clearly shows that for the first 3 years compounding annually is happening .
And for the last part 2/5 simple interest is happening but i am asking why we are doing simple interest
 
First, interest is a matter of contract. The math is determined by the correct legal interpretation of the contractual language. In countries with a legal system based on English common law, that interpretation will be based on principles of construing text, the law merchant, and supervening statute, regulation, and case law. The law merchant was customary law in most of Europe during the late medieval and early modern periods. To the best of my knowledge, absent specific contrary contractual verbiage, banks in the U.S. today compute interest exactly as did a bank in 14th century Florence such as the de Medici bank. The bank computes interest as simple interest on the balance owed. Periodically, interest is "credited," meaning added to the balance owed.

For 32 years at the bank that was my former employer, one of my responsibilities was to oversee the methods used by computer programs to compute interest (including complexities arising from fractional amounts, leap years, and cut-off times). The typical way that we calculated interest was that after close of business each day (effectively including Saturday and Sunday)the computer multiplyied the balance on which interest was due ("ledger balance" or "collected balance" depending on the type of account) times the quotient of the annual rate promised and either 365 or 366. The product was truncated at millionths of a dollar and then added to a running total called "accrued" interest. On the last day of the month, the running total was rounded to hundredths of a dollar using "half adjustment" and that rounded amount was added ("credited") to the amount on which interest was due. Then accrued interest was set to zero for the upcoming month.

In short, the bank did not use compounding in its actual computation of interest. It always used simple interest with special rules about truncation, rounding, leap years, when funds earned interest, cut-off times, etc. Now the bank did use compound interest formulas to approximate the results of that process. In fact that was one way to confirm that the computer programs were working properly.

Compound interest is merely a simple way to compute simple interest on a balance increasing periodically by a known rule while ignoring all practical complications.
 
Saumyojit said:
@Dr.Peterson
Each of those uses simple interest . How can each of those can be using simple interest . If u see P(1+r/100)^3 this is the formula of compound interest which clearly shows that for the first 3 years compounding annually is happening .
And for the last part 2/5 simple interest is happening but i am asking why we are doing simple interest
Click to expand...
Have you never been taught what compound interest is?

Compound interest is simple interest, repeatedly calculated and then added in to the principle. That's where the formula comes from. "Compounding" is the addition step; the interest is calculated the same way during each period, whether compounded or not.

I'll try this one more time before giving up on you. Here's how I'd introduce the idea to someone who had never learned about it.

Suppose we have 8% interest compounded annually for 3 2/5 years, starting with Rs 100. (I'm going to think of r as the decimal, 0.08 in the example, so I don't have to keep writing /100. This is much more natural to me, though evidently it is not what is taught in your country.)

Interest for the first year is calculated using the (simple) interest formula i = Prt as usual, and then added to the principal. So the interest is 100*8/100*1 = Rs 8, and the new principal is 100 + 8 = 108. So we are calculating simple interest for the year, then compounding by adding to the principal. But since P + Prt can be written as P(1 + rt), and t is one year, we can say that what we did was just to multiply P(1 + r), in this case multiply P by 1.08.

Interest for the second year is calculated using i = Prt again, and then added to the principal. So the interest is 108*8/100*1 = Rs 8.64, and the new principal is 108 + 8.64 = 116.64. We have multiplied a second time by 1.08.

Interest for the third year is calculated using i = Prt again, and then added to the principal. So the interest is 116.64*8/100*1 = Rs 9.33, and the new principal is 116.64 + 9.33 = 125.97. We have multiplied a third time by 1.08.

Interest for the final 2/5 year is calculated using i = Prt again. So the interest is 125.97*8/100*(2/5) = Rs 4.03, and the new principal is 125.97 + 4.03 = 130.00.

The calculation for the first three years can be combined into one operation, multiplying P by (1+r)^3. And in fact, 100(1.08)^3 = 125.97. Then the last part of a year can't be combined into that; this time we multiply by (1 + 0.08(2/5)) = 1.032, with the result being 130.00.

So we can think of the compound interest part as repeated simple interest, or we can use the formula to find that and then use simple interest directly for the last bit.
 
JeffM said:
First, interest is a matter of contract. The math is determined by the correct legal interpretation of the contractual language. In countries with a legal system based on English common law, that interpretation will be based on principles of construing text, the law merchant, and supervening statute, regulation, and case law. The law merchant was customary law in most of Europe during the late medieval and early modern periods. To the best of my knowledge, absent specific contrary contractual verbiage, banks in the U.S. today compute interest exactly as did a bank in 14th century Florence such as the de Medici bank. The bank computes interest as simple interest on the balance owed. Periodically, interest is "credited," meaning added to the balance owed.

For 32 years at the bank that was my former employer, one of my responsibilities was to oversee the methods used by computer programs to compute interest (including complexities arising from fractional amounts, leap years, and cut-off times). The typical way that we calculated interest was that after close of business each day (effectively including Saturday and Sunday)the computer multiplyied the balance on which interest was due ("ledger balance" or "collected balance" depending on the type of account) times the quotient of the annual rate promised and either 365 or 366. The product was truncated at millionths of a dollar and then added to a running total called "accrued" interest. On the last day of the month, the running total was rounded to hundredths of a dollar using "half adjustment" and that rounded amount was added ("credited") to the amount on which interest was due. Then accrued interest was set to zero for the upcoming month.

In short, the bank did not use compounding in its actual computation of interest. It always used simple interest with special rules about truncation, rounding, leap years, when funds earned interest, cut-off times, etc. Now the bank did use compound interest formulas to approximate the results of that process. In fact that was one way to confirm that the computer programs were working properly.

Compound interest is merely a simple way to compute simple interest on a balance increasing periodically by a known rule while ignoring all practical complications.
Click to expand...

I dont understand this passage .
 
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