What is the difference between the compound interest and simple interest on a sum of Rs 1000 at 10% interest for two years?

Saving

The power of compounding grows your savings faster

3 minutes

The sooner you start to save, the more you'll earn with compound interest.

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.

This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.

Save more with compound interest

The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.

For example, if you put $10,000 into a savings account with 3% interest compounded monthly:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r)n

A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02)

n = the number of time periods

How to calculate compound interest

To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:

1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042

2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24

3. Use the compound interest formula

A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106

A = $2,211.64

Lorenzo and Sophia compare the compounding effect

Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.

After five years:

• Sophia has $12,834.
• Lorenzo has $12,500.

Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

• Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan.
• Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent.
• Compound interest accrues and is added to the accumulated interest of previous periods, so borrowers must pay interest on interest as well as principal.

Simple interest is calculated using the following formula:

Simple Interest = P × r × n where: P = Principal amount r = Annual interest rate n = Term of loan, in years \begin{aligned} &\text{Simple Interest} = P \times r \times n \\ &\textbf{where:} \\ &P = \text{Principal amount} \\ &r = \text{Annual interest rate} \\ &n = \text{Term of loan, in years} \\ \end{aligned} ​Simple Interest=P×r×nwhere:P=Principal amountr=Annual interest raten=Term of loan, in years​

Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. For example, say a student obtains a simple-interest loan to pay one year of college tuition, which costs $18,000, and the annual interest rate on the loan is 6%. The student repays the loan over three years. The amount of simple interest paid is:

$ 3 , 240 = $ 18 , 000 × 0.06 × 3 \begin{aligned} &\$3,240 = \$18,000 \times 0.06 \times 3 \\ \end{aligned} ​$3,240=$18,000×0.06×3​

and the total amount paid is:

$ 21 , 240 = $ 18 , 000 + $ 3 , 240 \begin{aligned} &\$21,240 = \$18,000 + \$3,240 \\ \end{aligned} ​$21,240=$18,000+$3,240​

Compound interest accrues and is added to the accumulated interest of previous periods; it includes interest on interest, in other words. The formula for compound interest is:

Compound Interest = P × ( 1 + r ) t − P where: P = Principal amount r = Annual interest rate t = Number of years interest is applied \begin{aligned} &\text{Compound Interest} = P \times \left ( 1 + r \right )^t - P \\ &\textbf{where:} \\ &P = \text{Principal amount} \\ &r = \text{Annual interest rate} \\ &t = \text{Number of years interest is applied} \\ \end{aligned} ​Compound Interest=P×(1+r)t−Pwhere:P=Principal amountr=Annual interest ratet=Number of years interest is applied​

It is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods, and then minus the reduction in the principal for that year. With compound interest, borrowers must pay interest on the interest as well as the principal.

Below are some examples of simple and compound interest.

Suppose you plunk $5,000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you earn after one year would be $150:

 $ 5 , 0 0 0 × 3 % × 1 \begin{aligned} &\$5,000 \times 3\% \times 1 \\ \end{aligned} ​$5,000×3%×1​

Continuing with the above example, suppose your certificate of deposit is cashable at any time, with interest payable to you on a prorated basis. If you cash the CD after four months, how much would you earn in interest? You would receive $50: $ 5 , 0 0 0 × 3 % × 4 1 2 \begin{aligned} &\$5,000 \times 3\% \times \frac{ 4 }{ 12 } \\ \end{aligned} ​$5,000×3%×124​​

Suppose Bob borrows $500,000 for three years from his rich uncle, who agrees to charge Bob simple interest at 5% annually. How much would Bob have to pay in interest charges every year, and what would his total interest charges be after three years? (Assume the principal amount remains the same throughout the three years, i.e., the full loan amount is repaid after three years.) Bob would have to pay $25,000 in interest charges every year:

 $ 5 0 0 , 0 0 0 × 5 % × 1 \begin{aligned} &\$500,000 \times 5\% \times 1 \\ \end{aligned} ​$500,000×5%×1​

or $75,000 in total interest charges after three years:

 $ 2 5 , 0 0 0 × 3 \begin{aligned} &\$25,000 \times 3 \\ \end{aligned} ​$25,000×3​

Continuing with the above example, Bob needs to borrow an additional $500,000 for three years. Unfortunately, his rich uncle is tapped out. So, he takes a loan from the bank at an interest rate of 5% per year compounded annually, with the full loan amount and interest payable after three years. What would be the total interest paid by Bob?

Since compound interest is calculated on the principal and accumulated interest, here's how it adds up:

 After Year One, Interest Payable = $ 2 5 , 0 0 0 , or  $ 5 0 0 , 0 0 0  (Loan Principal) × 5 % × 1 After Year Two, Interest Payable = $ 2 6 , 2 5 0 , or  $ 5 2 5 , 0 0 0  (Loan Principal + Year One Interest) × 5 % × 1 After Year Three, Interest Payable = $ 2 7 , 5 6 2 . 5 0 , or  $ 5 5 1 , 2 5 0  Loan Principal + Interest for Years One and Two) × 5 % × 1 Total Interest Payable After Three Years = $ 7 8 , 8 1 2 . 5 0 , or  $ 2 5 , 0 0 0 + $ 2 6 , 2 5 0 + $ 2 7 , 5 6 2 . 5 0 \begin{aligned} &\text{After Year One, Interest Payable} = \$25,000 \text{,} \\ &\text{or } \$500,000 \text{ (Loan Principal)} \times 5\% \times 1 \\ &\text{After Year Two, Interest Payable} = \$26,250 \text{,} \\ &\text{or } \$525,000 \text{ (Loan Principal + Year One Interest)} \\ &\times 5\% \times 1 \\ &\text{After Year Three, Interest Payable} = \$27,562.50 \text{,} \\ &\text{or } \$551,250 \text{ Loan Principal + Interest for Years One} \\ &\text{and Two)} \times 5\% \times 1 \\ &\text{Total Interest Payable After Three Years} = \$78,812.50 \text{,} \\ &\text{or } \$25,000 + \$26,250 + \$27,562.50 \\ \end{aligned} ​After Year One, Interest Payable=$25,000,or $500,000 (Loan Principal)×5%×1After Year Two, Interest Payable=$26,250,or $525,000 (Loan Principal + Year One Interest)×5%×1After Year Three, Interest Payable=$27,562.50,or $551,250 Loan Principal + Interest for Years Oneand Two)×5%×1Total Interest Payable After Three Years=$78,812.50,or $25,000+$26,250+$27,562.50​

It can also be determined using the compound interest formula from above:

 Total Interest Payable After Three Years = $ 7 8 , 8 1 2 . 5 0 , or  $ 5 0 0 , 0 0 0  (Loan Principal) × ( 1 + 0 . 0 5 ) 3 − $ 5 0 0 , 0 0 0 \begin{aligned} &\text{Total Interest Payable After Three Years} = \$78,812.50 \text{,} \\ &\text{or } \$500,000 \text{ (Loan Principal)} \times (1 + 0.05)^3 - \$500,000 \\ \end{aligned} ​Total Interest Payable After Three Years=$78,812.50,or $500,000 (Loan Principal)×(1+0.05)3−$500,000​

This example shows how the formula for compound interest arises from paying interest on interest as well as principal.