how arithmetic and geometric progression can be used to solve problems related to banking business?
Arithmetic and geometric progressions, commonly known as sequences, are mathematical concepts that can be used to solve various problems in many fields, including banking business. Let's explore how these progressions can be applied in banking scenarios.
1. Interest Calculation:
Banking transactions often involve interest calculations. In particular, the concept of compound interest, where interest is earned on both the initial amount (principal) and the accumulated interest, can be modeled using geometric progressions. The formula to calculate the compound interest is:
Future Value = Principal * (1 + Rate)^Time
Here, the rate of interest represents the common ratio (r) in a geometric progression, while the time period corresponds to the number of terms (n) in the progression. By using this formula, banks can calculate the future value of an investment or loan.
2. Loan Repayment:
In the context of loans, banks often use arithmetic progressions to determine the equal installments (EMIs) that borrowers need to pay back over a fixed period. By dividing the principal plus the accruing interest over the loan period, banks ensure regular and manageable payments. The formula for calculating the EMI in an arithmetic progression is:
EMI = (P / n) + (P * r)
Here, P represents the principal amount, n denotes the number of installments, and r represents the rate of interest. By using this formula, banks can determine the installment amount that a borrower needs to repay regularly until the loan is cleared.
3. Savings and Investments:
Banks often encourage customers to save or invest their money to earn returns. In such cases, both arithmetic and geometric progressions can be utilized. For instance, if a customer chooses to invest in a fixed deposit (FD) account, the interest earned can be calculated using geometric progression. On the other hand, if a customer opts for a recurring deposit (RD), where they deposit a fixed amount each month, the maturity value can be calculated using arithmetic progression.
By employing these progression concepts, banks can effectively calculate interest, manage loan repayment structures, and estimate future account values. These mathematical tools are essential in financial calculations and aid decision-making processes in the banking sector.