Reducing Balance Method of Interest Calculation

How I learned about the reducing balance method of interest calculation? Its a story.

One day my friend got a call from a bank.

The person told him that the bank can offer personal loan @ 8.5% per annum.

He was very surprised to hear those figures.

His initial thought was that the person on line was bluffing.

But he just wanted to confirm few things before concluding.

He asked the person how he can offer personal loan at such low interest?

The person from bank said that @8.5% will be charged if loan is taken at fixed interest plan.

Interest @15.36% will be charged if loan is taken at reducing balance plan.

My friend became even more confused. He called me for the clarifications.

This is a common point of confusion for many people.

How banks can afford to offer personal loans only @8.5% fixed interest?

Whereas for reducing balance plan they charge interest as high as @15.36% per annum.

What is fixed interest plan?

Suppose a person took $100,000 personal loan @8.5% interest on fixed plan for one year.

As this is a fixed plan it means at the end of one year, total interest payable will be Rs 8,500.

The calculation of interest payable is simple, $100000×8.5/100 = $8500.

What is reducing balance plan?

Example 1:

Suppose a person took $100,000 personal loan @8.5% interest on reducing balance plan for one year.

In this case a fixed EMI of $8722 will be payable by the person each month.

If the person pays $8722 for next 12 month, total payment done is $8722×12=$104,664.

Effective rate of interest paid by the person is (104664-100000)/100000=4.664% per annum.

Compare this with fixed interest plan.

Person paid $8500 (@8.5% per annum) at end of year in fixed plan.

While he paid only $4664 (@8.5% per annum) at end of year in reducing balance plan.

Reducing balance plan is a much better option of availing bank loans.

Example 2:

Suppose a person took $100,000 personal loan @15.36% interest on reducing balance plan for one year.

In this case a fixed EMI of $9042 will be payable by the person each month.

If the person pays $9042 for next 12 month, total payment done is $9042×12=$108,500.

Effective rate of interest paid by the person is (108500-100000)/100000=8.5% per annum.

Compare this with fixed interest plan.

Person paid $8500 (@8.5% per annum) at end of year in fixed plan.

While he again paid only $8500 (@15.36% per annum) at end of year in reducing balance plan.

It means, though interest charged in reducing balance plan was 15.36%, but effective interest paid was equivalent to 8.5% interest of fixed plan.

Why in reducing balance plan, person pays less interest?

The concept is very simple. Take less loan, pay less interest. Take high loan, pay higher interest.

Reducing Balance Method Interest Calculation

Loan of $100,000 personal loan @8.5% interest on reducing balance plan for one year

MonthPrincipalInterestTotal PaymentBalanceLoan Paid To Date
00.000.000.001,00,000.000.00%
128,014.00708.008,722.0091,986.008.01%
118,070.00652.008,722.0083,916.0016.08%
108,128.00594.008,722.0075,788.0024.21%
98,185.00537.008,722.0067,603.0032.40%
88,243.00479.008,722.0059,360.0040.64%
78,302.00420.008,722.0051,059.0048.94%
68,360.00362.008,722.0042,698.0057.30%
58,420.00302.008,722.0034,279.0065.72%
48,479.00243.008,722.0025,800.0074.20%
38,539.00183.008,722.0017,260.0082.74%
28,600.00122.008,722.008,661.0091.34%
18,661.0061.008,722.000.00100.00%
1,00,0004,6631,04,664
4.66%

Loan of $100,000 personal loan @15.36% interest on reducing balance plan for one year

MonthPrincipalInterestTotal PaymentBalanceLoan Paid To Date
00.000.000.001,00,000.000.00%
127,764.001,278.009,042.0092,236.007.76%
117,863.001,179.009,042.0084,373.0015.63%
107,963.001,078.009,042.0076,410.0023.59%
98,065.00976.009,042.0068,345.0031.66%
88,168.00873.009,042.0060,176.0039.82%
78,273.00769.009,042.0051,904.0048.10%
68,378.00663.009,042.0043,525.0056.47%
58,485.00556.009,042.0035,040.0064.96%
48,594.00448.009,042.0026,446.0073.55%
38,704.00338.009,042.0017,742.0082.26%
28,815.00227.009,042.008,928.0091.07%
18,928.00114.009,042.000.00100.00%
1,00,0008,5001,08,500
8.50%

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