What is the difference between simple interest and compound interest for a period of 2 years at a rate of 10% per annum?

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mtor

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt   = 20,000(1 + 0.085/12)(12)(4)   = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m   =   (1 + 0.098/12)12 - 1   =  0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P � r / [1 - (1 + r)-n]

D = P � (1 + r)k - R � [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x � P � r)] / log (1 + r)

Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i where i = r/m is the interest paid each period and n = m � t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =
5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12) = $23,763.28

Value of a Bond:

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the "what-if" scenarios by entering different numerical value(s), to make your "good" strategic decision.

Replace the existing numerical example, with your own case-information, and then click one the Calculate.

1. What is Simple Interest?
2. What is Compound Interest?
3. Difference Between Simple Interest and Compound Interest?

Interest is calculated on the investment or loan taken. There are two ways one can calculate interest. The two ways are simple interest (SI) and compound interest (CI). Simple interest is basically the interest on a loan or investment. It is calculated on the principal amount. At the same time, Compound Interest is the interest calculated on interest. It is calculated on the principal amount as well as the previous period’s interest. This article covers the difference between simple interest and compound interest in detail.

What is Simple Interest?

Simple interest (SI) is the cost of borrowing. It is the interest only on the principal amount as a percentage of the principal amount. Borrowers will benefit from simple interest as they have to pay interest only on loans taken. In other words, simple interest is the amount that one pays to the borrower for using the borrowed money for a fixed period.

One can easily compute Simple interest by multiplying the interest amount with the tenure and the principal amount. Simple interest doesn’t consider the previous interest. It is simply based on the original contribution amount.

Car loans and consumer loans use simple interest while estimating the interest payments. Even a certificate of deposit uses simple interest to calculate the return from the investment.

Borrowers benefit more from simple interest as there is no power of compounding. In other words, there is no interest on interest. However, investors might lose if their investments are based on simple interest.

What is the formula for Simple interest?

Simple interest is computed by multiplying the interest rate for a period by the principal amount and the tenure. The tenure can be in days, months, or years. Hence the interest rate has to be converted accordingly before multiplying with the principal amount and tenure.

One can use the following formula to calculate the simple interest:

Simple Interest = P*I*N

Where,

P – Principal Amount

I – Interest Rate for the period

N – Tenure

Example 1

Let’s understand simple interest with an example. Ms Devika invests INR 1,00,000 in a fixed deposit for a tenure of three years at a 7% interest rate. Using the formula of simple interest, we can calculate the interest Ms Devika will earn from the investment.

Simple Interest = INR 1,00,000*7%*3 years

Simple Interest = INR 21,000

For her investment, Ms Devika receives INR 21,000 at the end of three years (investment tenure). The bank or the financial institutions pays Ms Devika an interest of 7% for using her deposit amount for its operations during the tenure of her investment (three years). The INR 7,000 is the interest that Ms Devika receives on her deposit from the borrower.

The simple interest should be calculated according to the duration of the investment or loan. If a loan is only for a few days or months, the interest rate has to be converted into a daily or monthly basis. Let’s take an example of a loan that charges interest on a daily basis to understand it better. 

Example 2

The principal amount of a loan is INR 50,000, of tenure of 60 days, with an interest rate of 5% per annum. One can compute the simple interest, in this case, as follows.

Principal amount – INR 50,000

Tenure – 60 days

Interest rate – 5% per annum or 0.014% per day.

Simple interest = INR 410.95

Therefore, the total interest the borrower will pay for the INR 50,000 loan for a tenure of 60 days is INR 410.95.

It is important to note that the higher the amount, the higher will be the interest. Also, the higher the duration of the investments, the greater will be the interest.

What is Compound Interest?

Unlike simple interest, which gains interest only on the principal sum, compound interest (CI) earns interest on the previously earned interest. The interest is added to the principal amount. CI is simply Interest on Interest. The whole principle revolves around generating high returns by compounding the interest received on the principal sum. 

In other words, CI has the potential to earn more return than just the simple interest from an investment. The investments grow exponentially with compound interest because it is based on the principal power of compounding.

The bank or financial institution, or the lender decide on the frequency of compounding. It can be daily, monthly, quarterly, half-yearly or yearly. The higher the frequency of compounding, the higher will be the interest accrual amount. Hence, investors benefit from compound interest more than borrowers.

Banks use compound interest for some loans. But compound interest is most commonly used in investments. Also, compound interest is used by fixed deposits, mutual funds, and any other investment that has reinvestment of profits.

What is the formula for compound interest?

CI is calculated by multiplying one plus interest raised to the power of the compounding periods with the principal amount. Finally, the principal amount has to be subtracted to obtain the CI.

One can use the following formula to calculate compound interest:

A=P(1+r/n)^(n*t)-1)

Where,

A – Compound Interest

P – Principal Amount

r – the rate of interest

n – the number of compounding periods

t – number of years (duration)

Example 1

Let’s understand CI calculation with an example. Mr Charan invests INR 10,000 at the rate of 10% for five years. One can compute the CI using the formula.

A = 10000*((1+10%)^(5)-1)

A = INR 6,105.

The interest earned by Mr Charan is INR 6,105. The corpus at the end of his investment tenure is INR 16,105 (the principal and the interest). On the other hand, the simple interest for the same investment and tenure is INR 5,000. The difference between SI and CI amount is INR 1,105.

Example 2

If the frequency of compounding is higher, then the interest will be higher. Also, if the investment duration is higher, the returns will be higher as well. Let’s take the same example as above but with higher compounding periods to understand how the interest will be higher in this case.

Investment – INR 10,000

Interest – 10% per annum

Tenure – 5 years

Compounded – half yearly, therefore the compounding periods are 2

A = 10000*((1+10%/2)^(5*2)-1)

A = 10000*((1+5%)^(10)-1)

The CI in this case, for Mr Charan is INR 6289. The corpus at the end of his investment tenure is INR 16,289 (the principal and the interest). Mr Charan earned INR 183 extra in this case. Hence with higher compounding periods, the interest will also be higher.

Also, one can use the Scripbox’s Compound Interest Calculator to determine the values faster.

Explore Best Banks in India

What is the power of compounding?

Compounding refers to a scenario where interest earns interest. It simply means when earnings are reinvested, the initial investment and the reinvested earnings grow at a constant rate. This makes the investments multiply at a faster rate. This is called the power of compounding. The higher the compounding frequency, the higher will be the returns from the investment. Compounding frequency is the number of times the interest is calculated in a year.

Compounding is a compelling concept, and no wonder Albert Einstein called it the 8th wonder of the world. Under compounding, you can make your money work harder for you. The interest that accumulates earns more interest in the long term. Also, the longer you stay invested, the higher will be the return from an investment. Hence it is advisable to start investing at early ages to benefit from the power of compounding.

Difference Between Simple Interest and Compound Interest?

Following are the key differences between simple interest vs compound interest:

Explore Fixed Deposit Pages

What is the difference between simple interest and compound interest for a period of 2 years at a rate of 10% per annum on a sum of $60000?

What is the difference between simple interest and compound interest for a period of 2 years at rate of 10%?

What is the difference between simple interest and compound interest for a period of 2 years?

What will be the difference between simple and compound interest at the rate 10% per annum on the sum of rupees 1000 after 4 years?