### Interest Rate in APY

There is quite some buzz in market about the interest earnings of the contributions made towards the Atal Pension Yojana. While the APY is definitely a meaningful scheme for those who are from unorganized sector, the real bummer comes in when one looks at APY from the perspective of interest earnings.

*Interest calculation on APY*

Let us explain this with a quick mathematical illustration, which will in turn be based on a few assumptions. Let us begin with the assumptions:

- You are of age 30.
- You select the pension slab of ₹ 5,000 per month after retirement.

According to the scheme, if the above assumptions are true then,

- Your monthly contribution has to be ₹ 577.
- You need to pay this amount for 30 years straight.

At 8% market interest rate per year, the amount of money that is required to pay a pension amount of ₹ 5,000 per month is ₹ 7,50,000.

Here is the simple calculation:

Therefore, monthly interest earned will be:

This monthly interest is actually paid out as pension.

Now based on above assumptions, you will be paying ₹ 577 per month and earn a pension of ₹ 5,000 per month after paying for 30 years.

The total payment you actually make in 30 years will be:

That amount is way shorter that the amount required for the target pension amount. So, to reach the corpus of ₹ 7,50,000, your money will be put to work and interest will be accumulated. The accumulated interest will keep growing every year to eventually reach the target amount of ₹ 7,50,000. How much interest is required? Let us find out!

**Year 1**

Assuming that the annual interest rate is 7.37%, the total interest you earn in a single year is:

So, total money in your account after 1 year:

**Year 2**

You had 7430.83, you pay another 6924. So, the total interest you earn at the end of 2^{nd} year will be:

So, total money in account at the end of 2 years will be:

Thus, your account money keeps growing at a compounded rate.

So, the total money in your account after 30 years of payment using the compound rate formula

will be:

Year | Balance at end of year | New deposit in a year | Balance for calculating interest | Interest Earned | New Balance after interest |

1 | 6924 | 0 | 6924 | 510.2988 | 7434.2988 |

2 | 7434.2988 | 6924 | 14358.2988 | 1058.206622 | 15416.50542 |

3 | 15416.50542 | 6924 | 22340.50542 | 1646.49525 | 23987.00067 |

4 | 23987.00067 | 6924 | 30911.00067 | 2278.140749 | 33189.14142 |

5 | 33189.14142 | 6924 | 40113.14142 | 2956.338523 | 43069.47994 |

6 | 43069.47994 | 6924 | 49993.47994 | 3684.519472 | 53677.99942 |

7 | 53677.99942 | 6924 | 60601.99942 | 4466.367357 | 65068.36677 |

8 | 65068.36677 | 6924 | 71992.36677 | 5305.837431 | 77298.2042 |

9 | 77298.2042 | 6924 | 84222.2042 | 6207.17645 | 90429.38065 |

10 | 90429.38065 | 6924 | 97353.38065 | 7174.944154 | 104528.3248 |

11 | 104528.3248 | 6924 | 111452.3248 | 8214.036338 | 119666.3611 |

12 | 119666.3611 | 6924 | 126590.3611 | 9329.709616 | 135920.0708 |

13 | 135920.0708 | 6924 | 142844.0708 | 10527.60802 | 153371.6788 |

14 | 153371.6788 | 6924 | 160295.6788 | 11813.79153 | 172109.4703 |

15 | 172109.4703 | 6924 | 179033.4703 | 13194.76676 | 192228.2371 |

16 | 192228.2371 | 6924 | 199152.2371 | 14677.51987 | 213829.7569 |

17 | 213829.7569 | 6924 | 220753.7569 | 16269.55189 | 237023.3088 |

18 | 237023.3088 | 6924 | 243947.3088 | 17978.91666 | 261926.2255 |

19 | 261926.2255 | 6924 | 268850.2255 | 19814.26162 | 288664.4871 |

20 | 288664.4871 | 6924 | 295588.4871 | 21784.8715 | 317373.3586 |

21 | 317373.3586 | 6924 | 324297.3586 | 23900.71533 | 348198.0739 |

22 | 348198.0739 | 6924 | 355122.0739 | 26172.49685 | 381294.5708 |

23 | 381294.5708 | 6924 | 388218.5708 | 28611.70867 | 416830.2794 |

24 | 416830.2794 | 6924 | 423754.2794 | 31230.69039 | 454984.9698 |

25 | 454984.9698 | 6924 | 461908.9698 | 34042.69108 | 495951.6609 |

26 | 495951.6609 | 6924 | 502875.6609 | 37061.93621 | 539937.5971 |

27 | 539937.5971 | 6924 | 546861.5971 | 40303.69971 | 587165.2968 |

28 | 587165.2968 | 6924 | 594089.2968 | 43784.38118 | 637873.678 |

29 | 637873.678 | 6924 | 644797.678 | 47521.58887 | 692319.2669 |

30 | 692319.2669 | 6924 | 699243.2669 | 51534.22877 | 750777.4956 |

*PLEASE NOTE**: ABOVE CALCULATIONS ARE ROUGH ESTIMATES AND THERE MAY BE ERRORS. THE CALCULATIONS ARE USED FOR THE PURPOSE OF EXAMPLE ONLY AND DO NOT INDICATE FINAL CALCULATIONS MADE BY GOVERNMENT.*

So essentially, under Atal Pension Yojana, you will be paid an annual interest rate of 7.37% per year for achieving a corpus of ₹7.50 lakhs with monthly contribution of ₹577 for 30 years to earn a pension of 5,000 per month.

This interest rate is lower than the current interest rate the banks provide for Fixed Deposits. The current market rate is 8 to 8.5%. Using the above example when we calculate interest for different entry age and deposit period, the interest rate is always lower than current market rate. APY interest rates vary between 6.92% and 7.53% for the pension slab of ₹ 5,000. There may be slight variations for other slabs.

Funny that the above calculations did not account for inflation. Market interest rate grows with year-on-year inflation! Thus, instead of paying for APY, one can opt for fixed deposits.

However, what really makes sense is that the payments under APY are made each month, whereas for FD, you will have to pay the whole deposit amount at once! This is not possible for everyone.

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