In this article, we will be discussing all the formulas, tricks and problems for Simple and Compound Interest, one needs to know to solve questions based on this topic.

## Simple and Compound Interest Formula

Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit as in the case of a certificate of deposit. Interest can be calculated in two ways, simple interest or compound interest.

• Simple Interest: Compound interest is the addition of interest to the principal sum of a loan or deposit. Compound interest is calculated based on the principal, interest rate, and the time period involved.
• Compound Interest: The interest calculated on the amount initially invested or loaned. It is a method for calculating the interest earned or paid on a certain balance in a specific period.

There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound rather than simple basis. On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation.

### Simple Interest Formulas

When a person lends money to a borrower, the borrower usually has to pay an extra amount of money to the lender. This extra money is what we call interest. We can express this interest in terms of the amount that the borrower takes initially. If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest or the flat rate.

Simple Interest is calculated only on the principal amount (or on that portion of the principal amount which remains unpaid)

1) Simple Interest (SI) formula

where,

P – Principal or the original sum borrowed

R – Rate of interest. It is the rate at which the interest is calculated on the original sum

T – Time for which the original sum is borrowed. It is also denoted as ‘n’

2) Amount (A) = Principal + Simple Interest = P + (PTR)/100

Note: In simple interest, every year, the interest will be the same.

### Compound Interest Formulas

In the case of compound interest, the interest is added to the principal at the end of each period to arrive at the new principal for the next period. Under compound interest, the amount at the end of the first year will become principal for the second year; the amount at the end of the second year becomes the principal for the third year and so on.

##### Compound Interest – Annually
• Amount = P (1+r/100)t
• Compound Interest = Total amount – Principal
• Rate of interest (R) = [(A/P)1/ t − 1] %
##### Compound Interest – Half Yearly
• Amount = P (1+r/2/100)2t
• Compound Interest = Total amount – Principal
• Rate of interest (R) = 2*[P1/t − 1] %
##### Compound Interest – Quarterly
• Amount = P (1+r/4/100)4t
• Compound Interest = Total amount – Principal
##### Compound Interest – Monthly
• Amount = P (1+r/12/100)12t
##### Interest is Compounded Annually but Time is in Fraction, say 2(3/2) years
• Amount = P (1+r/100)* (1+(3/2)r/100)
##### Compound Interest when Rates are Different for Different Years
• Amount = P (1+r1/100) (1+r2/100) (1+r3/100)

### Tricks & Formulas for Simple Interest and Compound Interest

Here are some of the useful formulas of simple  and compound interest and tricks you need to remember while solving these problems.

1) If the interest is added to the principal every six months, then it is said to be compounded half-yearly or semi-annually or twice a year. The amount is calculated as

2) Similarly, if the interest is calculated and added four times in a year, then it is said to be compounded quarterly. The amount is calculated as

3) If the number of times of compounding in a year is increased to infinity, i.e., the interest is ‘compounding every moment’, the amount is given by

A = P.enr/100

### Simple and Compound Interest Questions

1) The population of a country is 10 crore and there is a possibility that the population will become 13.31 crore in 3 yr. What will be the annual rate percent on this growth?

Solution:

Given, P = 10 crore

and population after 3 yr = 13.31 crore

According to the formula,

Population after n yr = P (1 + R/100 )n

⇒ 13.31 = 10 (1 + R/100 )3

⇒ 1331/1000 = (1 + R/100 )3

⇒ (11/10)3 = (1 + R/100 )3

⇒ 1 + R/100 = 11/10

⇒ R/100 = 11/10 – 1 = 1/10

∴ R = 10%