I have a question about which compound interest formula is correct. If interest is compounded on a principal amount daily which formula do I use? I've have two different formulas. If compound interest rate is say at 10% and the principal amount is $100 why is the amount with one formula P(1+r/n)nt almost the same as the other if it were to be daily for 1 year as apposed to 1 time in one year. So you would have 2 problems. 1. would be 100(1+.1/365)365(1) =110.51 if compounded daily off this formula. 2. would be 100(1+.1/1)1 =110 take for instance 2 years on both instead. Daily one100(1+.1/365)365(2)=122.13 Annual one 100(1+.1/1)2=121 So that is an annual average of around 10% of the principal amount no matter if it is daily compounding or annual compounding? Maybe I'm miscontruing this but shouldn't compounded interest by definition be the percent of the principal amount plus the interest stacked on itself everytime it is compounded? For instance $100 at a 10% rate would be $110 if it was compounded once and $121 if compounded twice. So if you had a daily compounded interest shouldn't it be compounded at the same rate per day be increasing the frequency at which it is compound and not at a divided amount of the rate that it is done? Shouldn't compounded daily only affect the frequency in which it is compounded and end up being the other formula P[(1+i)n-1]. I know one is suppose to be and annual formula and the other is what you would use for daily, monthly, binannually. Which one is the right one to use? If the frequency is the only thing to change doesn't that mean that the formula P(1+r/n)nt isn't the right one to do when compounding interest daily?
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I have a question about which compound interest formula is correct. If interest is compounded on a principal amount daily which formula do I use? I've have two different formulas. If compound interest rate is say at 10% and the principal amount is $100 why is the amount with one formula P(1+r/n)nt almost the same as the other if it were to be daily for 1 year as apposed to 1 time in one year. So you would have 2 problems.
1. would be 100(1+.1/365)365(1) =110.51 if compounded daily off this formula.
2. would be 100(1+.1/1)1 =110
take for instance 2 years on both instead.
Daily one100(1+.1/365)365(2)=122.13
Annual one 100(1+.1/1)2=121
So that is an annual average of around 10% of the principal amount no matter if it is daily compounding or annual compounding?
Maybe I'm miscontruing this but shouldn't compounded interest by definition be the percent of the principal amount plus the interest stacked on itself everytime it is compounded? For instance $100 at a 10% rate would be $110 if it was compounded once and $121 if compounded twice. So if you had a daily compounded interest shouldn't it be compounded at the same rate per day be increasing the frequency at which it is compound and not at a divided amount of the rate that it is done?
Shouldn't compounded daily only affect the frequency in which it is compounded and end up being the other formula P[(1+i)n-1]. I know one is suppose to be and annual formula and the other is what you would use for daily, monthly, binannually. Which one is the right one to use? If the frequency is the only thing to change doesn't that mean that the formula P(1+r/n)nt isn't the right one to do when compounding interest daily?
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