There are a number of steps involved in the water cycle. Water passes through all three states of matter during this cycle. Natural forces such as the sun, air, land,…

## Simple Interest Vs. Compound Interest

Simple and compound interests are closely related to banking system, and they are the most basic maths we learn during our school classes. This article highlights the topic of simple interest vs. compound interest.

Suppose you have borrowed a certain sum of money or an amount from a bank as a loan, then you must be wanting to know what premium you have to pay as part of the loan repayment. The amount you need to pay as a repayment is generally calculated on the basis of compound interest. Mathematics has a lot of applications of simple interest vs. compound interest. This article gives you some detailed information about the same.

**Basics**

When some amount of money is borrowed, the interest is charged for the use of that money for a certain fixed period of time. When the time comes to pay the money back, the amount that was borrowed (called the principal) and the interest are paid back. The amount on which the interest will be incurred, depends on various factors like rate, the principal, and the time period for which the money was borrowed. Simple interest is generally used for a shorter duration of time, that means for a period of less than a year, like 40 days or 60 days.

**Formula**

Simple Interest (S.I) = *(P * R * T)/100*, where,

P = principal amount (the amount that was borrowed)

R = rate of interest (for one period)

T = time duration for which the money is borrowed (number of periods)

Let us understand this formula with the help of an example.

*Example*: John borrows a sum of USD 20, 000 for a period of 4 years at 8%, yearly interest. Find the interest and total amount due at the end of 4 years, that John is liable to pay.

*Solution*: We know that, *S.I = (P * R * T)/100*

Now, in this case , P = $20, 000, R= 8% = (8/100) = 0.08, T = 4 years,

Putting these in the formula, we get, S.I. = (20, 000 X 0.08 X 4) = USD 6400

Therefore, S.I. = USD 6400 and the Total Amount Due = Principal + S.I. = USD 20, 000 + USD 6400 = USD 26, 400.

So, John needs to pay USD 26, 400 at the end of 4 years.

**Vital Information**

Compound interest is calculated on the original principal, plus all the interest that has been accumulated for that period. It is just like a series of S.I.’s, where the interest occurred is added to the original principal, which is then considered as a principal for the next month or year. The striking difference between the two types is that in S.I., the principal amount is always fixed, but in C.I., the principal changes, as the interest for subsequent months is added to it. Generally, it is used to calculate the interests and rates for large period of times. In simple words, it incorporates an interest on the interest of all the prior periods.

**Formula**

Compound Interest (C.I) = *P(1+r/n) ^{nt}*, where,

P = principal amount, (either borrowed or deposited)

r = rate of interest (annual/quarterly/half-yearly)

n = numbers of times the interest is compounded every year

t = number of years (period) the amount is deposited for

To understand this more clearly, let’s see an example.

*Example*: Meredith borrows an amount of USD 1,000 from a bank and the bank charges a rate of 6%, compounded *quarterly*. Calculate the balance after 2 years.

*Solution*: Using the formula, we get,

P = USD 1000, R= 6% = (6/100) = 0.06, n = 4 (Remember, interest is compounded quarterly) and t = 2 years.

A = 1000(1 + 0.06/4)^{(4)(2)}

A= USD 1126.492 or USD 1126 (approximately)

So, the amount Meredith has to pay to the bank is USD 1610 and the compound interest incurred is,

C.I. = Amount (A) – Principal (P)

C.I= $1126.492 – $1000 = $126 (approximately)

If we compare the two, we will find that for the same sum of money deposited at the same rate for a fixed number of time, the C.I. is always greater than the S.I., (except in the first year, where they are equal if the frequency of compounding is annual).