Allow me to tell you a story about ‘reducing balance loan calculation’.

Why I’m writing a blog post about it?

Because it helped me and my friend to see the *reducing balance method* in a perspective of **cheap vs costly loans**.

First, I’ll tell you the story.

Then we will dig deeper into the reducing balance method of loan calculation.

That will explain how reducing balance method makes loan cheaper. Read more about how to prepare for loan application.

### The Story

One day my friend got a call from a bank.

He was told that the bank can offer personal loan @8.5% p.a. interest.

My friend was surprised. Why? Because normal personal-loan rate prevailing at that time was 14%+ per annum.

Hence my friend concluded that the call was spammy. [Read more about 5 Ways to Earn Higher Interest on FD’s]

But before he could disconnect the call, the bank personnel made two statements:

– Bank can offer loan @8.5% at ‘

fixed interest rate‘.– Bank can offer loan @14.88% at ‘

reducing balance rate‘.

Though these two statements made my friend even more confused, but he could say that at least the call is not spammy.

Anyways, he disconnected the call and reached me. Together we did some research. About what?

Why bank is offering such two distinct interest rates on the same loan?

## Fixed Interest vs Reducing Balance method

The bank was ready to offer personal loan @8.5% p.a., right?

When the market rate was 14%+, how bank was offering such low interest rates?

Actually the answer was hidden in the *two statements* made by the bank’s executive.

What we commonly see around is the ‘interest rates’ when loan calculation is done by ‘reducing balance method’.

But here 8.5% was offered at ‘fixed interest method’. [*Falling interest rates are not always bad: Read more about Dosa Economics of Raghuram Rajan*]

### #1. Fixed interest loan calculation…

Let’s see this example to know what is ‘fixed interest rate method’.

Suppose one took a personal loan of Rs.1,00,000, at 8.5% interest (@fixed rate) for 1 year.

The loan calculations will be as below:

Things to note in the above calculation:

**Interest Payable**: The total interest payable calculation is simple. But on downside, this simplicity makes the ‘fixed interest loans’ expensive for the borrowers. Calculation: Rs.1,00,000 x 8.5% x 1 year = Rs.8,500. Read about transfer of home loan for lower interest rates.**Total Payment**: The borrow has to repay the loan principal along with the interests for 1 year. Hence, the total payment due will be Rs.1,08,500 (Rs.1,00,000 + Rs.8,500). Read more about how to identify a debt trap.**Monthly Payments (EMI)**: The borrower has to pay Rs.1,08,500 in equal instalments paid each month. How many month the borrow has in hand? 12 months (1 year x 12 month). Hence, EMI (monthly payments) will be Rs.9,042 (Rs.1,08,500 / 12). Read more about habits of people with high credit score.

### #2. Reducing balance loan calculation

Here we will understand the difference between ‘fixed rate’ and ‘reducing balance rate’.

Let’s take the above example (in #1), but this time instead of interest rate being **fixed**, it will be **reducing balance**.

Loan of Rs.1,00,00 taken @8.5% interest (reducing balance) for 1 year.

This will be the loan calculation here:

Things to note in the above calculation:

**Monthly EMI**: In reducing balance method, interest calculation is complicated. Hence, we are using Excel to do the computation. First we will calculate the EMI. EMI calculation can be done using Excel’s PMT formula. Please note the difference in EMI between fixed (Rs.9,042) and reducing balance method (Rs.8,722). Read more about whether to invest money or use it to prepay loan?**Lower EMI:**In reducing balance method, the EMI is lower than fixed interest method. Why? Because unlike fixed interest method, here the interest calculation is done each month. As loan outstanding reduces each month, hence the borrower pays less interest each passing month. Read more about what to do when EMI is high.

Confused? Allow me to explain the reducing balance method of interest calculation using examples.

## EMI Calculator: Reducing Balance Loan Vs Fixed Interest Loan

#### Reducing Balance Loan Calculator

Principal Loan Amount (Rs.) | |

Interest Rate (%) | |

Time (in months) |

Total Interest (Rs.) :.. | |

Total Payment (Rs.) :.. | |

Monthly EMI (Rs.) :.. |

#### Fixed Interest Loan Calculator

Principal Loan Amount (Rs.) | |

Interest Rate (%) | |

Time (in years) |

Total Interest (Rs.) | |

Total Payment (Rs.) | |

EMI (Rs.) |

## Why in reducing balance method EMI is less?

For borrowers, reducing balance method is economical. How? Because they have to pay less EMI’s.

Why EMI is less? Because of the way the interest calculation is done.

To understand this, let’s take a simple example.

Loan of Rs.100,000 taken at 8.5% p.a. interest (reducing balance rate) for one year (12 months).

##### Calculation: Reducing balance method

Check how interest load gets lowered each month. How?

This happens because the interest calculation in done on the “loan balance” available that month.

As loan balance is reducing every passing month, interest on loan is accordingly reducing.

But this is not the case with ‘fixed interest method’. There the interest load remains the same even if the “loan balance” is falling.

##### Calculation: Fixed Interest method

Check how interest load remains same each month. Why?

This happens because the interest calculation in done based on the loan balance in the starting month.

No matter if the loan balance is reducing with EMI’s being paid, but the payable interest remains the same.

**Comparison between Reducing Balance and Fixed Interest calculations**

SL | Description | Reducing Balance Loans | Fixed Interest Loans |

1 | Offered Interest Rates on Loans | Higher | Lower |

2 | Calculation Process of Total Interest Payble on Loan | Complicated | Simple |

3 | Interest paid each month | Reduces with time | Remains constant with time |

4 | Interest calculated on which loan balance | Based on reducing loan balance | Based on loan balance of the first month |

5 | Principal paid | Same | Same |

6 | Total Interest Paid | Lower | Higher |

7 | Monthly EMI’s | Lower | Higher |

## Explanation: 14.88% Interest Vs 8.5% Interest rates…

Coming back to the story which was narrated in the beginning of the blog post.

Banks were ready to offer loan to my friend at two drastically different interest rates:

**@8.5% p.a**: Loan offered at Fixed Interest.**@14.88% p.a**: Loan offered at Reducing Balance Interest.

What was the logic of this loan offering? How the bank was able to offer such low interest rates?

The bank’s could offer such low interest (8.5% vs 14.88%) because they were making anyhow the same amount of money.

Check the interest calculation shown below:

Take-away’s from the above table:

**Reducing Balance Loan**: Though the visible interest rate of reducing balance loan is higher, but over a period of time, total payable by the borrower (principal + interest) is small.**Fixed Interest Loan**: Though the visible interest rate of fixed interest loan is small, but over a period of time, total payable by the borrower (principal + interest) is high.

## Conclusion

Reducing balance method is a more borrower friendly approach of interest calculation on loans. Why it is so?

Because when we pay EMI each month, there is a simultaneous reduction in loan balance. When loan balance reduces, the accrued interest must also fall.

Reducing balance method uses this philosophy to calculate the payable interest.

I hope I was able to give you a decent idea about the reducing balance method of loan calculation.

In case you have any query/feedback – please post it in the comment section below.

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## 29 Responses

This is so useful to consider taking loans as Sri Lanka is in dire straits and interest rates have gone through the roof! Keep up the good work.

This is how loan are on Whole Life insurance policies

In reducing method how do we get EMI amount and principal amount

Hi,

– EMI calculated is explained in point #2 above.

– Principal amount is the disbursed loan amount.

Thanks for asking

I get 1100000 Rs home loan in 180 month per month 16300 EMI

What interest I paid (loan is Flat Rate)

Loan amount 11000000

EMI per month 16300

Loan paid in 15 years

What interest I paid

Interest = Total Payment – Loan Amount = (16300x12x15 – 11,00,000) = 18,34,000

Thanks for asking.

Mani,

What about if there are a number of payments are missed? Or payments were not made on time? How do we then calculate?

*Because I’m now understanding that, even if no payment is made for months, the interest still has to be calculated and applied to the balance.

Please help me.

Good lecture!

However, I would like to request you to tell how we determine the monthly ‘principal installment’. Like how was rs 8,014 in the example above determined?.

Very useful… Thank you very much. Keep doing what is good for others, helping others and I believe good things will go back to you.

Please get in touch with me so that we can do some business together on some finance calculations.

Sir Can assist me to work out:

Loan : 324,000

Fixed 2.25% for 2 years

How to calculate the loan interest

Thank you for sharing this article! This is what I am looking for. Finally, I found it. Thank you once again.

Sir,

Please give me a calculation on the following data:

Loan amount: Rs.12 crore

Interest: 3.25 on reducing floating interest

Period: 10 years

Loan Payment: Yearly

Thanks,

Dr. Guha

Sir pl guide me as I am going to take car loan of rs630000

Fix %ofintrest 7.35 better or

Somehow similar reducing rate

Sir, i have availed housing loan (staff)for rs. 750000/= with 5% simple rate of interest on reduced balance for 240 months period. Every month 2450/= recovered. 240 months completed but loan was not closed. How sir

I have paid rs. 4250/= erroniouly mentioned as 2450/= sir

Simple Interest = 7,50,000 x 0.05 x 20 = 7,50,000

Total Payment Due = Principal + Interest = 15,00,000

Loan EMI = 15,00,000/(20 x 12) = Rs.6,250

What I’ve answered was based on SIMPLE INTEREST’s concept only.

I’ll need to know more about what was the terms of the “reduced balance”…to attempt that as well.

Sir, thanks for your prompt reply. But the reply was not salved the problem.

750000/= 1st month principle

745500/= 2nd month principle

741000/= 3rd month principle

Like that @ 5% interest apply on only monthly principle amount

THEN HOW MANY YEARS TO CLOSE THE LOAN

Rs 4500/= reduced from principal every month. Kindly help sir,

EMI calculation on “Simple Interest” rates are not done like this. Please see my previous reply.

very nicely explained ,thank you

If someone takes a loan @8% simple interest for Rs 770000 on condition that pricipal amount will be repaid by 92 monthly instalments @Rs 8378 and thereafter the interest to be repaid 60 monthly instalments.How mach interest to be paid?

Simple Interest = 770000 x 8% x (92+60)/12 = Rs.7,80,267

The interest amount of Rs.7,80,267 to be paid back in 60 monthly instalments (@13,004 per month)

really very helpful blog with all maths explained in detail.

good information thanks for posting

Thanks

I Think You Are a Good Teacher

Thanks for liking the work.

it is usefull