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It seems that there’s a shut connection between investing and borrowing (getting a mortgage). These acquainted with the formulae would let you know that they’re similar! Right here is how a house mortgage EMI will be understood when it comes to a lump sum and month-to-month SIP funding.
Suppose we would like a mortgage of Rs. 10, 00,000 (10L) from a financial institution at an annual rate of interest of 10%. That is how the financial institution will calculate the equated month-to-month instalment or the EMI.
You need 10L from the financial institution. As a substitute of giving this cash to you, if the financial institution had invested it on the price of 10% a 12 months for 30 years, it will get
1000000 x(1+ 10%/12)^360 = 19837399.4 (198.37 Lakhs)
Right here 10%/12 is the month-to-month rate of interest, and 360 = length in months (30 x 12).
If the financial institution has to lend 10L to you, it’s going to purpose to obtain 198.37L from you over 30 years on the similar rate of interest, payable every month.
You’ll not be paying 198.37L to the financial institution, however you may be paying a month-to-month quantity, which, if invested on the similar price, would fetch the financial institution 198.37L after 30 years.
Due to this fact, so far as the financial institution is worried, the EMI is a month-to-month SIP acquired from you for 30 years, calculated within the following manner:
What quantity do you have to make investments every month on the price of 10% a 12 months in order that after 30 years, the funding worth is 198.37L? Ring a bell?
This query could be acquainted to anybody who has used a monetary purpose calculator. That is the calculation:
19837399.4 = SIP x [(1+10%/12)^360-1]/(10%/12)
That is inverted to calculate the SIP = 877.5.7 ~ 8776.
Due to this fact, the financial institution units the EMI as 8776.
The mortgage EMI calculation is derived within the following manner:
19837399.4 = EMI x [(1+10%/12)^360-1]/(10%/12)
1000000 x(1+ 10%/12)^360 = EMI x [(1+10%/12)^360-1]/(10%/12)
Thus the mortgage calculation will be considered as an funding equation:
Lump sum funding worth = SIP funding worth
Now, 1000000 = P = mortgage quantity
10%/12 = R = rate of interest monthly
360 = n = length in months
So now we have, P x(1+ R)^n = EMI x [(1+R)^n-1]/R
Due to this fact, EMI =P x R x(1+ R)^n / [(1+R)^n-1]
In abstract, the EMI is a month-to-month SIP acquired from you over the mortgage tenure.
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