Question

Find the output of the program given below. 10 Read \(P, N, R\) 20 Data \(2000,2,20\) 30 Let \(A=P\left[(1+R / 100)^{N}\right]\) 40 Print \(A\) 50 END (1) 3240 (2) 2880 (3) 3840 (4) 3360

Short answer

Answer: (2) 2880

Step-by-step solution

Identify the given data

The data given in the program is P = 2000, N = 2, and R = 20.

Analyze the formula

The formula is \(A=P\left[(1+R / 100)^{N}\right]\). We will now calculate the value of A using the given data (P = 2000, N = 2, and R = 20).

Calculate the value of A

\(A = 2000\left[(1+20 / 100)^{2}\right] = 2000\left[(1+0.20)^{2}\right] = 2000\left[(1.20)^{2}\right] = 2000 \times 1.44 = 2880\)

Determine the output of the program

The value of A is calculated to be 2880. Hence, the program's output is the second option given: (2) 2880

Key concepts

Data Reading in Programming

Understanding how data is read and used in a programming language is essential. In most programs, data reading involves retrieving information from a predefined source or user input to use it in calculations or processes. In the exercise, the program reads the values of three variables: \( P \), \( N \), and \( R \).
The command 'Read' instructs the program to take these values from an external list or input. Here, the values are predefined as \( P = 2000 \), \( N = 2 \), and \( R = 20 \). These values are crucial for further calculations. Being familiar with data reading commands helps you understand how initial conditions or parameters are set in various programs.

• Read command: Extracts input data.
• Data command: Supplies specific data points (e.g., \( P, N, R \)).

Learning to effectively read and interpret data inputs is foundational to developing successful programs.

Formula Analysis

In programming, formulas are often used to perform specific calculations. These usually involve mathematical expressions that use variables and arithmetic operations. The given formula is \( A = P\left[(1+R / 100)^{N}\right] \), which is an expression used to calculate compound amounts or similar scenarios in financial mathematics.
Let's break down the formula:

• \( P \) is the principal amount or the initial value.
• \( R \) represents the rate of interest expressed as a percentage.
• \( N \) indicates the number of periods or years for which the calculation is done.
• The portion \( (1+R/100)^N \) calculates the growth factor over \( N \) periods.

This formula demonstrates how change in value can be modelled over time, showing the power of programming for complex calculations. Understanding the function of each component within the formula allows programming students to adapt and apply such calculations in multiple scenarios.

Mathematical Calculation Steps

Breaking down complex calculations into simpler steps can make them easier to tackle. In the exercise, the calculation of \( A \) is done using a step-by-step approach:
1. Substitute the values: First, replace \( P, N, \) and \( R \) with their respective values: 2000, 2, and 20.
2. Calculate the rate increment: Compute \( 1 + R / 100 \), which becomes \( 1 + 0.2 = 1.2 \).
3. Apply the power: Raise the result to the power of \( N \), which is \( (1.2)^2 = 1.44 \).
4. Final calculation: Multiply \( P \) by the result: \( 2000 \times 1.44 = 2880 \).

• Makes it easier to manage each step independently.
• Ensures accuracy when handling more complex calculations.

Understanding each step in sequence not only improves clarity but also avoids errors by allowing verification at each stage, which is a critical skill in both programming and mathematics.