The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
Suppose you want to run a cupcake business, but you do not have the money to start. You can borrow money from a bank or a trusted individual in such situations, promising to return the funds. The money you borrow is called a loan that you get on certain terms and conditions. In commercial mathematics, the ‘principal’ is the amount of money you initially borrowed from the bank for a particular period.
The bank provides the principal amount only when you pay the interest amount. Interest is the extra amount you pay the bank on the money borrowed. You will have to pay the interest till you return the entire principal money borrowed initially. Hence, in banking terms, you (the borrower) pays the ‘Amount’ (Principal + Interest) to the bank.
Amount = Principal + Interest
Rate of Interest = % of the principal paid to the bank as interest for a specific period.
Example: If you borrow ₹ 10,00,000 from the bank (Principal) and you pay ₹ 1,00,000 per annum as interest:
The rate of interest = 10%.
Since 10/100 x ₹ 10,00,000 = ₹ 1,00,000.
The rate of interest is usually calculated per year/per annum.
Simple interest is calculated based on the initial principal. It is denoted as S.I.
Formula: S.I. = (P x R x T)100
Where,
P = Principal (initial)
R = Rate of interest
T = Time period (in years)
Generally, simple interest is paid per annum. The additional amount payable by the borrower does not change every year in the case of simple interest.
Compound interest differs from simple interest since compound interest means adding the interest amount that hasn’t yet been paid to the initial principal amount. If you took a loan for your cupcake business and couldn’t pay the interest amount, instead of charging simple interest for both years, the bank adds the first year’s interest to the following year’s principal amount. Hence, for year 1, you pay simple interest, but for year two, the interest is compounded as the principal amount is increased. The difference between the final amount paid by the borrower and the initial principal borrowed is called Compound Interest.
Compound Interest Calculator (C.I) = Final Amount (payable) – Initial Principal
C.I. = A – P
Where,
A = Final amount
P = Initial Principal
Compound Interest Formula :
Here,
A = Amount
P = Principal
R = Rate of compound interest per annum
N = Number of years
Compound interest changes every year because the principal grows every year. Let us solve an example to understand this concept better. Remember the cupcake business? The rate of interest was 10% for year 1. Let’s say that instead of charging simple interest, the bank charged compound interest. Hence,
P = ₹ 10,00,000
R = 10%
N = 1 year
Therefore, according to the compound interest calculator,
A = ₹ 10,00,000 x [1 + 10/100]¹
A = ₹ 11,00,000
Thereby,
C.I. = A – P
Compound Interest = ₹ 11,00,000 – ₹ 10,00,000 = ₹ 1,00,000.
But, C.I. for year 2 will be
A²(Amount for Year 2) = P x [1 + R/100]² = ₹ 10,00,000 x [1 + 10/100]²
A² = ₹ 10,00,000 x 1.21
Amount for Year 2 = 12,10,000
Therefore, C.I. = ₹ 12,10,000 – ₹ 10,00,000 = ₹ 2,10,000
Whereas, simple interest for 2 years = (P x R x T)100= (₹ 10,00,000 x 10 x 2) 100
S.I. = ₹ 2,00,000
Compound interest is more than the amount of simple interest payable for more than a year.
In business terms, growth may mean inflation, growth in business profits, or an enterprise’s growth.
Growth is calculated using the compound interest formula.
Growth after n years = initial production value x [1 + r/100]^n
where r = rate of growth in production %
The growth rate formula can also be used to calculate the population growth rate.
Depreciation is the loss incurred by a business over a specific period. The amount of decrease in the value of production is called depreciation.
Depreciation = initial production value x [1 – r/100]^n
Where r = rate of loss %.
To conclude, commercial mathematics is used by buyers, sellers, lenders, and borrowers. That accounts for pretty much the entire human population. Simple and compound interests are different kinds of interests the borrower pays against the principal amount borrowed. Simple interest is the additional amount paid based on the principal amount, whereas compound interest is paid based on the principal and the accumulated interest over a period.