Interest is the price paid for using money over time. In business and finance, interest connects money with time value:
Where it is used (exam points):
Quick conversions:
In simple interest (SI), interest is calculated only on the original principal.
Formulas:
Example: P = 10,000, R = 12% p.a., T = 2 years I = (10,000×12×2)/100 = 2,400 A = 10,000 + 2,400 = 12,400
In compound interest (CI), interest is calculated on principal plus accumulated interest.
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Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
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Interest is the price paid for using money over time. In business and finance, interest connects money with time value:
Where it is used (exam points):
Quick conversions:
In simple interest (SI), interest is calculated only on the original principal.
Formulas:
Example: P = 10,000, R = 12% p.a., T = 2 years I = (10,000×12×2)/100 = 2,400 A = 10,000 + 2,400 = 12,400
In compound interest (CI), interest is calculated on principal plus accumulated interest.
A = P (1 + R/100)^T CI = A − P
If compounded n times per year:
A = P (1 + (R/100)/n)^(nT)
EAR = [ (1 + (R/100)/n)^n − 1 ] × 100
PV is today’s value of a future amount.
PV = FV / (1 + R/100)^T
Discount factor = 1 / (1 + R/100)^T
Example: FV = 20,000, R = 10%, T = 2 PV = 20,000/(1.10)^2 = 20,000/1.21 ≈ 16,529
FV is the value of a present amount after earning interest.
For CI: FV = P (1 + R/100)^T For SI: FV = P [1 + (R×T)/100]
From this topic
Given P = 12,000, R = 8% p.a., T = 3 years.
SI, I = (P×R×T)/100 = (12,000×8×3)/100 = 2,880. Amount, A = P + I = 12,000 + 2,880 = 14,880.
So, SI = ₹2,880 and Amount = ₹14,880.
P = 10,000, R = 10%, T = 2.
Amount A = P(1+R/100)^T = 10,000 × (1.10)^2 = 10,000 × 1.21 = 12,100. CI = A − P = 12,100 − 10,000 = 2,100.
So, CI = ₹2,100 (Amount = ₹12,100).
Present value (PV) is today’s value of a future amount found by discounting. For annual compounding: PV = FV / (1 + R/100)^T.
Future value (FV) is the value of a present sum after earning interest: FV = P (1 + R/100)^T.
Relationship: FV = PV × (1 + R/100)^T and PV = FV / (1 + R/100)^T.
Example: PV of ₹20,000 due after 2 years at 10% is PV = 20,000/(1.10)^2 = 20,000/1.21 ≈ ₹16,529. So ₹16,529 today becomes ₹20,000 after 2 years at 10%.