Calculate the amount of Rs 12000 for 2 years at 10 per annum compound interest

Complete step-by-step answer:
We know that the amount ‘A’ at the end of ‘n’ years at the rate of r% per annum when the interest is compounded annually is given by,
$A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}...........\left( i \right)$
Where P = Initial amount or principal amount that increases by r % annually.
Here, we have 12000 as the principal amount which is increasing at a rate of 12% for the time period of 10 years.
Hence, from the given equation, we have
P = 12000 Rs
r = 12%
n = 10 years
Now, using the equation, we can get amount ‘A’ after 10 years as,
$\begin{align}
  & A=12000{{\left( 1+\dfrac{12}{100} \right)}^{10}} \\
 & A=12000{{\left( 1+\dfrac{3}{25} \right)}^{10}} \\
\end{align}$
Now, taking LCM inside the bracket, we get
$A=12000{{\left( \dfrac{28}{25} \right)}^{10}}...........\left( ii \right)$
Now, we can solve equation (ii) by multiplying $\dfrac{28}{25}$ to 10 times. But this process would be very lengthy for calculating the value of ‘A’.
So, we can use logarithm and antilogarithm to get value of A as follows
Taking log to both sides to equation (ii), we get.
$\log A=\log \left( \left( 12000 \right){{\left( \dfrac{28}{25} \right)}^{10}} \right)..........\left( iii \right)$
We can use identity of logarithm as
log ab = log a + log b
Applying above identity with equation (iii) we get,
$\log A=\log 12000+\log {{\left( \dfrac{28}{25} \right)}^{10}}$
Now, we can use another identity of ‘log’ as
$\log {{m}^{n}}=n\log m$
So, we get
$\log A=\log 12000+10\log \dfrac{28}{25}........\left( iv \right)$
We have another identity of logarithm
$\log \left( \dfrac{a}{b} \right)=\log a-\log b$
Hence, equation (iv) can be given as
$\log A=\log 12+\log 1000+10\left( \log 28-log25 \right)$
Now, we get values of logarithms of above by using logarithm table as
log 28 = 1.4472
log 25 = 1.3979
log 12 = 1.0792
log 1000 = $\log {{10}^{3}}$ = 3log 10 = 3
Hence, on putting values in above equation, we get
log A = 4.0792 + 0.493
log A = 4.5722
Taking antilog to both sides, we get
A = antilog (4.5722) = 37350
So, the amount after 10 years is Rs 37350.
As we know compound interest can be given by relation.
Compound interest = Total amount after interest – principal value/amount.
So, compound interest after 10 years is,
 37350 – 12000 = Rs.25350

Note: One may apply the formula of simple interest as $\dfrac{P\times R\times T}{100}$ where ‘P’ is principal amount, ‘R’ is interest and ‘T’ is time period but that has become wrong. So, be clear with both terms i.e simple and compound interest. One can answer compound interest as ‘A’ i.e. total amount after 10 years. So, don’t confuse compound interest and total amount.

Principal for the first year = Rs 12000

Rate of interest = 10% p.a.

Interest for the first year = Rs (12000 × 10 × 1) / 100

= Rs 1200

Amount at the end of first year = Rs 12000 + Rs 1200

= 13200

Principal for the second year = Rs 13200

Interest for the second year = Rs (13200 × 10 × 1) / 100

= Rs 1320

Amount at the end of second year = Rs 13200 + Rs 1320

= Rs 14520

Principal for the third year = Rs 14520

Interest for the third year = Rs (14520 × 10 × 1) / 100

= Rs 1452

Amount at the end of third year = Rs 14520 + Rs 1452

= Rs 15972

Hence,

Compound interest for 3 year = Final amount – (original) Principal

= Rs 15972 – Rs 12000

= Rs 3972

For Ist year

Principal (P) = Rs.12,000

Rate (R) = 10%

Time (T) = 1 year

I = Interest =`(12,000xx10xx1)/100`

= 120 × 10

= Rs.1200

Amount = P + I = Rs.12,000 + Rs.1200 = Rs.13,200

For IInd year

P = Rs.13,200, R = 10%, Time (T) = 1 year

∴ Interest =`(13,200xx10xx1)/100` = 132 × 10 

= Rs.1320

∴ Amount in 2 years = Rs. (13,200) + (1320)

= Rs.14520

Compound interest in 2 years = Rs.1200 + Rs.1320 = Rs.2520

[or directly = Rs.14520 − Rs.12000 = Rs.2520]

House Rent Allowance means, if you are a salaried person and staying in a rented accommodation, then you can claim tax exemption for the rent paid. The rent can be partially or fully tax exempt.

Who can claim HRA exemption?

Self-employed and salaried people can claim HRA exemption, though under a different section of Income-tax as explained in the article.

HRA Exemption Section

House Rent Allowance (HRA) is exempted under section 10(13A) of the Income Tax Act.

Also Read – How to download LIC premium Receipts Online

House Rent Allowance rules and regulations

Under House Rent Allowance rules and regulations, you will get exemption up to a minimum of the following 3 amounts:

1. Actual House Rent Allowance (HRA) received by the employee in the year.
2. Rent paid by the employee for his accommodation in excess of 10% of his salary.
3. 50% of the salary, if he stays in any of the 4 metro cities of Delhi, Mumbai, Kolkata or Chennai; otherwise, 40% of the salary.

The salary for this calculation means the basic salary which includes dearness allowance if the terms of employment provide for it and commission based on a fixed percentage of turnover achieved by the employee.

Please note that if the employee is staying in his own house or not paying any rent, he will not be eligible for the above tax exemption.

HRA Calculation in Excel 2020-21

You can click on the below link and download HRA calculation in Excel for 2020-21

HRA Calculation in Excel 2019-20

House Rent Allowance (HRA) – Factors Deciding Exemption

From the above rules, it is clear that there are 4 factors which decide your eligibility for House Rent Allowance (HRA) exemption. They are:

1. Actual HRA received by you
2. Actual Rent paid by you
3. Your city of residence
4. Your salary (Basic Pay & DA)

HRA Calculation in Excel – Exemption Calculator for AY 2021-22

Let us see an example of how you can do HRA calculation in Excel. The Excel can be used as HRA exemption calculator for AY 2021-22.

Suresh is getting a Basic Pay of Rs. 50,000 per month and House Rent Allowance (HRA) of Rs. 20,000 per month. He is staying in rented premises in Chennai and is paying a monthly rent of Rs. 22,000.

How is HRA calculated?

HRA is calculated as per the 3 formulas given below:

1. Actual HRA received in a year = 12 x 20,000 = 2,40,000
2. Rent – 10% of the salary in a year = 12 x (22,000 – 10% of 50,000) = 2,04,000
3. 50% of the salary in a year = 50% of 12 x 50,000 = 3 Lakhs

Suresh is eligible for a deduction of Rs. 2,04,000 from his actual HRA of Rs. 2,40,000. So, he needs to pay tax for the balance of Rs. 36,000 only.

House Rent Allowance (HRA) Tax Benefits – Lose without Landlord’s Pan

The Circular (08/2013) states that “…an employee claiming exemption from tax with respect to House Rent Allowance received is now required to report the PAN of the landlord to the employer, if the rent paid by the employee to the landlord exceeds Rs. 1 Lakh per annum, along with the rent receipt.”

In simple words, if the annual rent is above Rs. 1 Lakh, then the employee must report the PAN details of the landlord to the employer. If the landlord is not having a PAN,then the landlord must submit a declaration to this effect along with his name and address.

The step is to plug 2 loopholes in the system:

1. To stop the abuse of House Rent Allowance (HRA) claims
2.  Furnish the correct rent income information by the landlord

These are the basics of House Rent Allowance exemption; In addition to the basics, now let us answer a few common questions asked by the readers…

Can you claim HRA if you own a house?

The answer to this question is both – Yes and No.

• You cannot claim house rent allowance (HRA) if you are staying in your own house.
• You can claim HRA if you are staying on rent, not in your own house.

Can you claim both HRA and Home Loan for Tax Exemption?

If you are paying the loan for your own house and staying in a rented accommodation, you can claim the tax benefits for both, HRA as well as the Loan property.

Can HRA be claimed by both the husband and wife?

Yes, HRA can be claimed by both the husband and wife if:

• Both husband and wife, are paying rent to the landlord.
• Husband and wife are giving separate receipts for the rent paid to the landlord

The husband and wife can claim HRA exemption proportionately but both can not claim the entire rent paid to landlord.

Is HRA compulsory?

No, HRA is not compulsory because it depends upon your employer to make house rent allowance as a part of your salary.

Can husband pay rent to wife and claim HRA?

Yes, the husband can pay rent to wife and claim HRA in case the wife owns the house. The same would be clubbed into the wife’s income under the head (Income from House Property) and taxed accordingly.

But if the wife is not having any income and the house has been bought by you for her, the income will be clubbed in your income and taxed accordingly.

Can I pay rent to my mother/brother/parents and claim HRA?

Yes, you can claim HRA if you are paying rent to your mother, brother or parents but they need to show the income as Income under House Property.

Is rent agreement mandatory for HRA exemption?

No. Rent agreement is not mandatory for HRA exemption but it is better to have one as your CA can demand it for lower TDS.

Is rent receipt mandatory for HRA exemption?

If you are paying rent up to Rs. 3,000, rent receipt is not mandatory for house rent allowance exemption, but for rent above Rs. 3,000, rent receipt is mandatory for HRA exemption. Also, rent above Rs. 1 lakh per annum will require a PAN card of the landlord.

What is 80GG claim deduction for HRA?

Section 80GG applies for HRA claim deduction under the following conditions:

• If your employer does not include HRA in your salary, and
• Self employed people

You can still claim deduction under 80GG.

Read this article

HRA rent receipt format in India

There is no particular HRA rent receipt format in India, You can add following details in the rent receipt:

• Landlord’s Name
• Address
• Duration
• Rent amount
• PAN card number, if annual rent is more than Rs. 1 Lakh

Probably I have included all points in this article, but if I have missed any point please let me know. I would be happy to include them in the article.

What is the compound interest on Rs 12000 for 2 years at 10% per annum compounded annually?

How much will 12000 amount to in 2 years at compound interest?

How much compound interest will be on 14000 Rs for 2 years at 10% per annum compounded?

What is the compound interest on Rs 10000 for 2 years at rate of interest 10% per annum?