# Declining Balance Interest Calculation

#### **Declining Balance—Equal installments**

The declining balance method calculates interest at periodic intervals on the amount of the principal not yet repaid. 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 repayments amounts don’t change, the proportion of principal and interest components changes with time. With each successive repayment, 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 an 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

{% hint style="info" %}
The way to apply payments is as follows:

Calculate interest in the principal due: If balance = $1000, and i = 0.025, interest is $25\
Calculate the amount to principal which is the monthly payment minus the interest due: $518.83 - $25 = $493.83\
Calculate the principal remaining, which is the previous principal remaining minus the amount applied to principal: $1000 - $493.83 = $506.17 (remaining balance)\
Once next payment is received, repeat steps 1 to 3.
{% endhint %}
