Question

Write a program to compute the total amount payable with annual interest for a given number of years. The inputs are principal amount, rate of interest and number of years. Attempt the program with or without recursion.

Short answer

Create a program using the compound interest formula to compute the total payable amount.

Step-by-step solution

Understand the Problem

The problem requires calculating the total amount payable on a principal amount with a given annual interest rate over a specified number of years. This can be achieved using the formula for compound interest or simple interest, but since no specific method is mentioned, we will use the standard compound interest formula.

Gather Information

Identify the inputs required for the calculation. We need the principal amount, the annual interest rate, and the number of years.

Use the Compound Interest Formula

The compound interest formula is: \( A = P(1 + r)^n \), where \( A \) is the amount, \( P \) is the principal amount, \( r \) is the annual interest rate in decimal form (interest rate divided by 100), and \( n \) is the number of years. This formula will give us the total amount payable after the specified number of years.

Implement the Program

Create a program (using Python or any other language) that accepts the principal, rate, and years as input and computes the total amount using the compound interest formula. ```python def compute_total_amount(principal, rate, years): total_amount = principal * (1 + rate / 100) ** years return total_amount # Example principal = 1000 # Principal amount rate = 5 # Annual interest rate years = 10 # Number of years amount_payable = compute_total_amount(principal, rate, years) print(f'Total amount payable: {amount_payable:.2f}') ```

Verify the Output

Run the program with example input values of your choice to verify that it correctly calculates the total amount payable. For instance, with a principal of 1000, rate of 5%, and duration of 10 years, the amount should be correctly computed by the program.

Key concepts

Principal Amount

In the realm of finance, the principal amount refers to the original sum of money that is invested or loaned. When you calculate compound interest, it serves as the base amount on which the accrued interest is computed over a specified period.
For instance, if you deposit $1000 in a savings account, that $1000 is your principal. This amount remains crucial in our calculations as it directly influences the final amount received after accruing interest.
In the case of our program, we input this principal amount, aiming to determine how much it will grow considering the specified interest and time.

Interest Rate

The interest rate is a critical factor in determining the growth of your principal amount. It represents the percentage at which your investment grows annually. This rate is usually expressed as a percentage, but for calculations, it needs to be converted to a decimal.
For instance, an interest rate of 5% translates to 0.05 in decimal form.

• Higher interest rates mean faster growth of your investment.
• Interest rates can be simple or compounded — in our context, we focus on compounded.

Ensuring you understand how this percentage affects your return is essential for sound financial planning. It enables accurate predictions of future investment values.

Number of Years

The number of years indicates how long your money will be invested or lent. It is crucial to understand how this period affects the total amount payable using compound interest.
Over time, as interest is computed on both the principal and the accumulated interest from previous years, the amount grows larger due to what is known as "compounding."
Longer periods typically result in more significant returns because the interest has more time to accumulate.

• Long-term investments usually yield higher returns.
• Short-term investments may be less profitable but are more liquid.

So, understanding your investment timeline is key in financial calculations and planning.

Python Programming

Python is a versatile programming language often used for financial computations due to its simplicity and rich ecosystem. In this context, we use Python to compute the compound interest by implementing a straightforward function.
The code breaks down as follows:

• A function, `compute_total_amount`, is defined to calculate the compound interest using the formula.
• We pass in the `principal`, `rate`, and `years` as parameters.
• Python handles the calculations through arithmetic operators and the power operator `**`.
• Finally, the computed amount is stored in a variable and printed, formatted to two decimal places for clarity.

This solution demonstrates not only how Python can handle financial calculations but also how understanding key parameters leads to more informed decisions.