A new accurate formula to calculate maturity of recurring deposit

Purpose of literature

 

First of all I was planning to invest with recurring deposit, for this I went to XYZ bank to ask the details regarding recurring deposit there executive said you can find every details like maturity amount, interest rate on internet when I saw on net then found that the maturity amount given by bank on recurring deposit and the calculations of maturity amount done by me manually is not match to each other, there is a slight difference in both of the maturity value. After that I started calculating manually the maturity value of some other banks, then also I found out that there is difference in maturity amount given by bank and the manual calculations done by me. Then I studied deeply and found out that the

formula which is used by maximum bank is so I calculated from this formula also and found that the value occurred by this formula is different (less) then manual calculations

There are some banks also who gives the maturity amount less than the maturity amount occurred by formula used by bank all and all maximum banks are giving less maturity amount from the amount I have calculated manually

There are 1 or 2 banks who are giving more maturity value then the manually calculated value this clears that no bank is giving the exact maturity value of recurring deposit

 

The main purpose of my literature is to give the correct formula to calculate maturity amount of recurring deposit to bank and for the customers to earn the actual interest

To innovate the correct formula of recurring deposits I have two task in front of me the first one was that how the formula that banks are using had come and second was to find the error in that. After doing the deep study of the formula I understand that how the formula has come

In below I try to explain in detail:-

We know that    is the formula to calculate the final amount on the basis of quarterly compound

interest.

Where,

A= Final amount

P= principal amount

r= rate of interest per annum

n= number of times interest is compounded quarterly

 

Suppose that r/400=i and P=R we have done this to reach bank’s formula now we can write for the calculations of maturity amount of recurring deposits

 

As we know that   

=    

we know that

Putting the value of   in equation 1

 

Taking L.C.M











(Because interest is compounded quarterly)

My first task is completed

Now my second task is to find the error in this formula

To explain this I will give an example first:

Suppose Aman had invested 10000 at the rate of 8% per annum on the basis of quarterly compounded interest for 5 months then calculate the final amount

We know that  and this formula is used by bank

Where P=10000, r= 8, and n=5/3

Putting the value A=10335.55

According to me this calculation is wrong because the value of n should be in whole number fNow we use the Rajendra formula

Note: (this formula gives you the highest accuracy to occur the final amount of fixed deposit.)

Where

A=final amount

P=principal amount

R=rate of interest (for quarterly R/4)

n=number of times interest is compounded (where n is a whole number)

N=remaining months (after calculating n)

m= Brij Value

for quarterly 3

for monthly 1

for half yearly 6

for yearly 12

 

P=10000                                               N=2

R=8/4                                                    m=3

n=1

Putting the value

In the end we can say that the formula which is used by bank to occur the maturity value of recurring deposits where base n does not belong to the whole number that’s why this formula has an error.

Theory

We know that, to calculate the final amount of compound interest we have two formulas and they both give same value of final amount

First :-

Where,

A=Final amount

P=principal amount

R=Rate of interest per annum (for quarterly R/4, for half yearly R/2, for yearly R/1, for monthly R/12)

n= Number of periods

Second:-

Where,

A=Final amount

P=principal amount

r=Interest rate per annum (decimal)

n=Number of times interest is compounded per year

t=time (year)

 

To calculate the maturity amount of recurring deposit we can use any of the formula out of these two

We are using    to calculate the maturity value of recurring deposit

 

 

First of all we have to keep in mind that the value of n should be in whole number

After deep studies I have found the most accurate formula for maturity value of recurring deposit which Calculate the recurring deposit maturity value on the basis of any compounded interest from 1 to n number of months. My formula gives highest accuracy of maturity value of recurring deposit.

Note:- we will use I in my formula instead of P

My Rameshta formula for maturity value of recurring deposit is given below:-

Rameshta formula:-

Where,

M=Maturity value of recurring deposit

m= Brij Value

for monthly 1, for quarterly 3, for half yearly 6, and for yearly 12.

I=installment

R=rate of interest (Quarterly=R/4, half yearly= R/2, yearly = R/1, monthly=R/12)

N=remaining months (after calculating n)

n=Number of times interest is compounded

Note: N and n should always be in whole number

When interest is compounded quarterly then R=R/4 and m=3 now the formula will look like this

When interest is compounded half yearly then R=R/2 and m=6, now the formula will look like this:-

When interest is compounded yearly then R=R/1 and M=12 now the formula look like this:-

When interest is compounded monthly then R=R/12 and m=1 and N=0 now the formula will look like this:-

Now in below I have given two example of occurring maturity value through Rameshta Formula

For example:-

1- Apurva invested 10000 Rs per month for 24 months at the rate of 6.75% per annum on the basis of quarterly compounded what will be the maturity amount for recurring deposit?

• Using Rameshta formula:-

Where R= R/4 and m=3

For quarterly compounded interest

Where I=10000, R=6.75%, n=8, N=0 now putting the value

This is the final maturity value of above question for recurring deposit if we calculate manually the maturity value will be same.

For example 2

2- Arpit invested 5000 Rs per month in recurring deposit for quarterly compound basis on interest with 6.25% per year for 14 months then what will be the maturity value for this recurring deposit?

• Using Rameshta formula:

Where R= R/4 and m=3

For quarterly compounded interest

Where I=5000, R=6.25%, n=4, N=2 now putting the value

 

This is the final maturity value of above question for recurring deposit if we calculate manually the maturity value will be same.

My Rameshta formula is made by 2 parts

1st part is =

2nd part is=

Note: 1st part is only required to calculate the maturity and 2nd part is only used when N is required.