Question

hi guys....
shortcut method to learn simple interest & compound interest....
it's very important guys...
please help me...
if u given a right solution, I will follow u & mark u as brilliant.. ​

Answer 1

Step-by-step explanation:

1. Let principal =P; time =n years; and rate = r% per annum and let A be the total amount at the end of n years, then. ..
2. When compound interest reckoned half yearly, then r% become r/2% and time n become 2n; ...

For quarterly.

3. The difference between compound interest and simple interest over two years is given by.

hey neenga Tamil ah :)

Answer 2

Answer:

Before determining the reason of this why? Let’s first know what is interest and these interest rates?

Interest is the amount charged by the lender from the borrower on the principal loan sum. It is basically the cost of renting money. And, the rate at which interest is charged on the principal sum is known as the interest rate. The rate at which interest is charged depends on two factors

The value of money doesn’t remain same over time. It changes with time. The net worth of ₹ 100 today will not be same tomorrow i.e. If 5 pens could be bought presently with a INR 100 note then in future, maybe only 4 pens can be bought with the same ₹ 100 note. The reason behind this the inflation or price rise. So, the interest rate includes this factor of inflation

The credibility of the borrower, if there is more risk and chance of default on borrower’s part then more interest will be charged. And, if there is less chance of payment failure on the part of borrower then the rate of interest would be lower.

The above two reason becomes the basis of why interest rates are so important and have a great effect on markets and economy.

These concepts are categorized into type of interests

Simple Interest

Compound Interest

Let’s first start and understand Simple Interest because as the name suggests it is simple and comparatively easy to comprehend.

Simple interest is that type of interest which once credited does not earn interest on itself. It remains fixed over time.

The formula to calculate Simple Interest is

SI = {(P x R x T)/ 100}

Where, P = Principal Sum (the original loan/ deposited amount)

R = rate of interest (at which the loan is charged)

T = time period (the duration for which money is borrowed/ deposited)

So, if P amount is borrowed at the rate of interest R for T years then the amount to be repaid to the lender will be

A = P + SI

Consider a basic example of SI to understand the application of above formula such as Find the simple interest on ₹ 68000 at 16 2/3 % p.a. for 9 months.

Here, P = ₹68000

R = 162/3 % = 50/3% p.a.

T = 9 months = 9/12 years = ¾ years

SI = (68000 x 50/3 x ¾ x 1/100) = ₹8500

Compound Interest

This the most usual type of interest that is used in the banking system and economics. In this kind of interest along with one principal further earns interest on it after the completion of 1-time period. Suppose an amount P is deposited in an account or lent to the borrower that pays compound interest at the rate of R% p.a. Then after n years the deposit or loan will accumulate to:

P(1+R/100)n

Consider this example, if an amount of 100 is deposited in saving bank account for 3 years at the interest rate of 6% p.a. Then, after one year the ₹100 will accumulate to ₹106. Since in compound interest, interest itself earns interest, therefore, after 1-year interest for the 2nd will be calculated on ₹106 unlike to that of Simple interest where interest will be calculated on ₹100 only. Thus, after the end of the third year the total amount will become ₹100(1.06)3 = ₹119.1016.

IMPORTANT FORMULAS

When the interest is compounded Annually:

Amount= P (1 + R/100) n

When the interest is compounded Half-yearly:

Amount = P (1 + (R/2)/100)2n

When the interest is compounded Quarterly:

Amount = P (1 + (R/4)/100)4n

When the rates are different for different years, say R1%, R2% and R3% for 1 year, 2 years and 3-year resp. Then,

Amount = P (1 + R1/100) (1 + R2/100) (1 + R3/100)

Present worth of ₹ x due n years hence is given by:

Present worth = x/ (1 + R/100)n

If a certain sum becomes “x” times in n years, then the rate of compound interest will be

R = 100(x1/n – 1)

If a sum of money P amounts to A1 after T years at CI and the same sum of money amounts to A2 after (T + 1) years at CI, then

R = (A2 – A1)/ A1 x 100

Miscellaneous Examples of application of Compound Interest

Question 1: A man invests ₹ 5000 for 3 years at 5% p.a. compounded interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of third year.

Sol: Here, P = ₹5000, T = 3 years, r = 5%

Therefore, Interest at the end of 1st year = 5000 (1 + 0.05) – 5000 = ₹250

Now Income tax is 20% on the interest income so the leftover interest income after deducing income tax = (1 – 0.2) * 250 = ₹200

Total Amount at the end of 1st year = ₹5000 + 200 = ₹5200

Interest at the end of 2nd year = 5200 (1 + 0.05) – 5200 = ₹260

Interest income after Income tax = 0.8 * ₹260 = ₹208

Total Amount at the end of 2nd year = ₹5200 + 208 = ₹5408

Interest at the end of 3rd year = ₹5408 (1.05) – 5408 = ₹270.4

Interest income after Income tax = 0.8 * ₹270.4 = ₹216.32

Total Amount at the end of 2rd year = ₹5408 + 216.32 = ₹5624.32