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In Loan products - Interest method, which are the formulas used for calculating "Flat interest" and "Declining Balance"

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**Answer** by sangamesh
·
Feb 28, 2014 at 09:59 AM

**Flat Interest**

Flat interest refers to charging interest on the full original loan amount, rather than on the declining balance.

**Formula:- **

** Interest = P r/100 n**

**Interest Installment = "Total interest" divided by "# Of Repayments".**

**PPI = "Principal" divided by "# Of Repayments"**

Where,

P = loan amount- Initial amount

r = rate of interest per year/per month

n = term of the loan (Fraction of a year, i.e., 1/12 = 1 month, 1/52 = Week; If "Interest calculation period" is selected as "Daily" then 7/365 = Week)

For example, a client borrows a loan of $1000 with a interest rate of2% per month for four months.

This means that a $1000 principal amount lent is multiplied by 2/100, and then by 4 months to come up with $ 80 in total interest. Thus, $ 270 would be repaid over four months in equal installments.

**Answer** by sangamesh
·
Feb 28, 2014 at 10:24 AM

**Declining Balance - Equal installments**

Interest is computed 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.

**Formula:**

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

Where,

P = Loan amount

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

For example, a client borrows a loan of $1000 with a interest rate of5% per year with 2 instalments 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

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.

Note: Due to rounding of computed values, it could potentially be off by a maximum of N number of pennies after the full term of the loan. It will never be short if we round up, rather, principal could end up with a few more pennies.

**Answer** by bonnymwas
·
Oct 11, 2016 at 02:38 PM

Hi @sangamesh, I have an issue with how the reducing/declining balance is calculated. In this photo, I have a loan of 5,000 as shown on a 1.5% monthly reducing balance. The schedule is as shown above. The first repayment is okay in terms of calculation but from there, its all haywire.

For instance, let's take the repayment number 2 assuming that will are following this schedule to the letter. Our outstanding loan balance is 4,575 having paid the first installment. From this information, the interest on the second payment is supposed to be 0.015 * 4575 = 68.625. What is given on the schedule is 70.84. Why the difference? Am I the one doing something wrong, is this an error or why the discrepancy?

I have reproduced this issue on the local and demo platforms.

screen-shot-2016-10-11-at-161830.png
(185.5 kB)

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