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Interest is an essential element of every financial system and if we talk about interest what comes in mind is Compounding interest and Simple interest. Compounding interest offer interest on re-invested amount of interest. Compounding interest assume the re-invest the outstanding interest amount at the same rate.
Theorem:
"Effect of compounding over simple interest is much higher in long run because of exponential effect of time and rate difference"
What is Power of compounding?
Power of Compounding means study of exponential growth of interest. There are two factor affect the exponential growth of interest
1. Time phase
2. Interest rate
Lets understand with one example:
Compounding factor: What is it?
This is the measurement of exponential element in interest over and above simple interest rate.
To explain the effect of time, lets understand with the help of one example. Assume that interest rate of 5%. Initially compounding factor under both the system (simple interest and compounding interest) are more or less equal but after 30-40 years same is highly differentiating.
Lets analysis this case in detail:
Refer the Tab <% of Differential Factor>, Up to 30 Years amount of differential factor is below 100% but after that same is increase more than 100% every time as the component of interest in total outstanding amount is more than principle amount.
Hence over a period of time the effect of compounding due to increase in interest component is higher.
Formulas to analyse the impact of Time on compounding:
1. Incremental Compounding Factor:
This is the effect of time over change in interest rate. We know the interest rate change have lesser effect in initial period and same is increase with exponential growth over a period of time. We analyse the effect of minor change in interest rate how the ultimate result will change in following example:
Here I use two interest rate compounding annually, 5.00% and 5.50% that is 0.05% difference in two rate.
Initially up to 30 years incremental interest factor is less than 1 but after 30 years same is more than 1 . But surprising thing is growth rate is increase at reducing rate.
Formulas to analyse the impact of Rate on compounding:
1. Incremental Compounding Factor:
Use: Use to analyse the effect of higher compounding rate of interest over lower compounding rate of interest
2. Increment Compounding Factor for range of time:
Interest
Interest is an essential element of every financial system and if we talk about interest what comes in mind is Compounding interest and Simple interest. Compounding interest offer interest on re-invested amount of interest. Compounding interest assume the re-invest the outstanding interest amount at the same rate.Theorem:
"Effect of compounding over simple interest is much higher in long run because of exponential effect of time and rate difference"
Power of compounding:
What is Power of compounding?
Power of Compounding means study of exponential growth of interest. There are two factor affect the exponential growth of interest
1. Time phase
2. Interest rate
Time phase:
Initially time has minor exponential effect on growth rate of interest element. But with passage of time interest compounding actually higher than simple interest as amount of interest portion in total outstanding amount increases at increasing rate.Lets understand with one example:
Compounding factor: What is it?
This is the measurement of exponential element in interest over and above simple interest rate.
To explain the effect of time, lets understand with the help of one example. Assume that interest rate of 5%. Initially compounding factor under both the system (simple interest and compounding interest) are more or less equal but after 30-40 years same is highly differentiating.
Lets analysis this case in detail:
Refer the Tab <% of Differential Factor>, Up to 30 Years amount of differential factor is below 100% but after that same is increase more than 100% every time as the component of interest in total outstanding amount is more than principle amount.
Hence over a period of time the effect of compounding due to increase in interest component is higher.
Formulas to analyse the impact of Time on compounding:
1. Incremental Compounding Factor:
CF (t) = [(1+i)^n]/[(1+i)*n]*100
Where CF (t) = Incremental Compounding Factor of time
n = Time
i = Rate of interest
Use: Use to analyse the effect of compounding interest over simple interest
2. Increment Compounding Factor for range of time:
CF (t) = [(1+i)^n]-[(1+i)^(r-1)]/[(1+i)*n]-[(1+i)*(r-1)]*100
Where CF (t) = Incremental Compounding Factor for range of time
n = Time up to which analysis is required
i = Rate of interest
r= time from which analysis started
Use: As we know that interest rate is exponential to time and hence for analyzing the effect of interest rate over a particular period of time we use above formula.
Interest Rate
Over the period of time the some change in interest rate have larger impact on value of investment because of interest rate compounding factor.This is the effect of time over change in interest rate. We know the interest rate change have lesser effect in initial period and same is increase with exponential growth over a period of time. We analyse the effect of minor change in interest rate how the ultimate result will change in following example:
Here I use two interest rate compounding annually, 5.00% and 5.50% that is 0.05% difference in two rate.
Initially up to 30 years incremental interest factor is less than 1 but after 30 years same is more than 1 . But surprising thing is growth rate is increase at reducing rate.
Formulas to analyse the impact of Rate on compounding:
1. Incremental Compounding Factor:
CF (t) = [(1+ih)^n]/[(1+il)^n]*100
Where CF (t) = Incremental Compounding Factor of time
n= Time
ih = Higher rate of interest
il = Lower rate of interest
2. Increment Compounding Factor for range of time:
CF (t) = [(1+ih)^n]-[(1+ih)^(r-1)]/[(1+il)*n]-[(1+il)*(r-1)]*100
Where CF (t) = Incremental Compounding Factor for range of time
ih = Higher rate of interest
il = Lower rate of interest
r= time from which analysis started
n = Time up to which analysis is required
Use: As we know that interest rate is exponential to time and hence for analyzing the effect of interest rate over a particular period of time we use above formula.
For Investor and Financial Institution return of compounding interest is much greater in long run. and hence people prefer long term investment in debt market.
Compounding effect only prove true if investor re-invest the interest element.
For Investor and Financial Institution return of compounding interest is much greater in long run. and hence people prefer long term investment in debt market.
Compounding effect only prove true if investor re-invest the interest element.
Thanks and Keep Reading!!
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