PCPA Full Form

What is the full form of PCPA?

PCPA is a mathematical term that stands for Per Cent Per Annum. It is used to find the rate of interest over a particular period of time. It consists of two terms, namely, percent and per annum, each meaning a very particular mathematical formulation. The equation for PCPA can be used for calculating simple interest as well as compound interest. In this article, we will see what PCPA means mathematically and how it can be used to find the annual rate of interest through some examples.

Per Cent

The first part of PCPA stands for "per cent," where cent stands for 100. It is a number or ratio expressed as a factor of 100. A per cent number is dimensionless.

Example:

The per cent of 50 in 1550 can be calculated as:

\frac{50}{1150}\times100

Which equals 4.34%

Per Annum

Per annum means yearly or annually. It is a Latin term. Per annum in a practical sense means a recurring occurrence throughout different years. For example, if a bank charges 2% interest per annum, every year the interest will remain at 2% and the additional 2% payment should be made each year until the payment is settled.

Here are some examples of how to use per annum:

• A monthly payment of Rs.10 is to be made for a subscription. So, annually, you have to pay Rs.120 as the total cost.

• If you have to pay Rs.12000 in instalments over 10 years, dividing 12000 by 10, you have to pay 1200 every year for 10 years.

• If the maintenance cost for a machine is Rs.3000 per annum, you have to pay that amount every year.

• If the monthly interest rate of a credit card is 1.2%., by multiplying it by 12 months, we get the interest rate per annum which is 14.4%.

Simple Interest

Simple interest is calculated when you get a loan. A bank or money lender can fix a rate or an amount as the interest over a particular period, and you have to pay the amount until you return the borrowed amount.

For example, if you get a loan of Rs.30000 from a bank at a 3% per annum interest rate for 3 years, the total amount you have to pay back can be calculated using the simple interest formula.

The simple interest formula is:

SI=\frac{PTR}{100}

Where

SI= Simple Interest

P= Principal amount

T=Time period (in years)

R= Rate of interest (in per cent)

In the above example, P=30000, R=3 and T=3

So, SI=Rs. 2700

The total amount that has to be paid back after a certain time period is

Amount(A) = Principal(P) + Simple Interest (SI)

So, here A = 30000+2700= Rs.32700

Per cent per annum is used to find simple interest by identifying the rate of interest as the R mentioned in the simple interest equation is the same as per cent per annum.

Compound Interest

Compound interest is also used when we borrow or loan money or have to pay an interest amount in addition to the principal amount. The difference between simple interest and compound interest is that in compound interest, the per annum interest rate changes, unlike in simple interest.

For example, If a person borrows Rs. 4000 from a bank with 6% annual interest compounded quarterly, how much should he pay back after 5 years?

In compound interest, the total amount that has to be paid back after a certain time period is:

A=P\times\left ( 1+\frac{r}{n} \right )^{nt}

Where,

A = total amount that has to be paid back after a certain time period

P = principal amount

r = rate of interest (in percent)

n = number of times interest is compounded per year

t = time (in years)

The compound interest can be calculated as:

Compound Interest (CI) = Amount (A) - Principal Amount(P)

In the above example, P=4000, r=6, t=5, n=4

After substituting, the amount payable after five years is A= Rs. 5387.42