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Declining Balance—Equal installments

Interest is computed The declining balance method calculates interest at periodic intervals on the amount of the original principal that has not yet been repaid. Since the borrower only pays interest on that amount of original principal that has not yet been repaid, interest paid is smaller every period. However, to make sure that the borrower sets EMI.

Formulas:

EMI FORMULA Repayment amounts, EMI, are equal. The interest component of the EMI is larger in the initial repayments and gradually reduces over time when compared to the principal amount. The exact percentage allocated towards payment of the principal depends on the interest rate. Even though periodic EMI payment don’t change, the proportion of principal and interest components will change with time. With each successive payment, more is allocated towards the principal and less towards interest.

The calculations is:

EMI = i*P / [1- (1+i)^-n]

Where,

P =

loan amount (principal)
r =

rate of interest per year/per month
n =

term of the loan in periods
l =

length of a period (Fraction of a year, i.e., 1/12 = 1 month, 1/52 = Week;If Interest calculation period is Daily then 7/365 = Week)
i = Interest rate per period (r*l)

Note: Interest = Principal balance*i

Example

A client borrows a loan of $1000 with a interest rate

of 5% per year with 2

installments for every six months.

P=1000, r = 5/100, l = 6/12 & n = 2, i = 5/100 * 6/12 = 0.025
EMI = 0.025 * 1000 / [1-(1+0.025)^-2]
EMI = $518.83

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