Write a program that implements a user defined function that accepts Principal Amount, Rate, Time, Number of T

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Q. Write a program that implements a user defined function that accepts Principal Amount, Rate, Time, Number of Times the interest is compounded to calculate and displays compound interest. (Hint: CI=P*(1+r/n)^nt)

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Concept understanding — Simple Interest Calculation

Simple Interest: The Cost of Borrowing (or the Reward for Saving)

Imagine you lend a friend ₹100. A year later, they return the ₹100. You're even — but you also missed the chance to use that ₹100 yourself for a whole year. That inconvenience has a price. In finance, that price is called interest.

Simple interest is the most straightforward way to calculate that price. It says: the interest you earn (or pay) each year is a fixed percentage of the original amount you started with — no matter how many years pass.

The Core Intuition

Think of it like renting money. If you rent a car for a day, you pay a fixed daily rate. If you rent it for 5 days, you pay 5 times that daily rate. Simple interest works the same way:

The Principal (P) is the amount you lend or borrow — the "car."
The Rate (R) is the daily rental charge, expressed as a percentage of the car's value — the "rent per day."
The Time (T) is how many days you keep the car — the number of years.

The total rent (interest) is just: daily rent × number of days.

The Precise Statement

\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}

Where:

P = Principal (the original sum of money)
R = Rate of interest per year (in percent)
T = Time period (in years)

The Total Amount (A) you get back (or owe) at the end is:

A = P + \text{SI}

Why Divide by 100?

The rate $R$ is given as a percentage — say 10%. "10% per year" means you get ₹10 for every ₹100 you lend, each year. So for a principal $P$ , the interest for one year is:

\frac{10}{100} \times P = 0.10 \times P

That's the same as $\frac{P \times R}{100}$ . For $T$ years, you multiply by $T$ , giving $\frac{P \times R \times T}{100}$ .

A Worked Example

You deposit ₹2000 in a bank that offers 8% simple interest per year. You leave it for 3 years.

P = ₹2000
R = 8
T = 3

\text{SI} = \frac{2000 \times 8 \times 3}{100} = \frac{48000}{100} = ₹480

So after 3 years, you earn ₹480 in interest. Your total amount becomes:

A = 2000 + 480 = ₹2480

Tip

Notice that each year you earn exactly the same interest: $\frac{2000 \times 8}{100} = ₹160$ . Year 1: ₹160, Year 2: another ₹160, Year 3: another ₹160. The interest never grows because it's always calculated on the original ₹2000, not on the growing balance.

The Key Property (and its Limitation)

Simple interest is linear — the interest grows at a constant rate each year. This makes it easy to calculate and understand. …

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Define a function taking Principal, Rate (% p.a.), Time (years) and n (compoundings per year). The hint's formula P*(1+r/n)^(nt) gives the total amount; compound interest = amount − principal.

def calcCI(principal, rate, time, n):
    amount = principal * (1 + rate / (n * 100)) ** (n * time)
    ci = amount - principal
    print("Total amount     :", round(amount, 2))
    print("Compound interest:", round(ci, 2)) …

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Wrap the compound-interest formula in a user-defined function with four parameters (P, R, T, n); the hint's expression P*(1+r/n)^(nt) yields the total amount, so the interest itself is amount minus principal.

The idea. A user-defined function lets us name a computation once and reuse it with any values. The four inputs the question demands become the four parameters. One subtlety: the hinted formula

A = P * (1 + r/n) ** (n*t)      # r as a fraction, i.e. rate/100

is the maturity amount, not the interest. Compound interest is CI = A - P. Since the user enters the rate as a percentage, we divide by n * 100.

def calcCI(principal, rate, time, n):
    """Compute and display compound interest.
    rate is % per annum; n = number of times compounded per year."""
    amount = principal * (1 + rate / (n * 100)) ** (n * time)
    ci = amount - principal
    print("Total amount     :", round(amount, 2))
    print("Compound interest:", round(ci, 2))

p = float(input("Enter principal amount: "))
r = float(input("Enter rate of interest (% per annum): "))
t = float(input("Enter time (in years): "))
n = int(input("Enter number of times interest is compounded per year: "))
calcCI(p, r, t, n)

Key lines

(1 + rate/(n*100)) ** (n*time) — the growth factor applied n*t times (** is Python's power operator).
round(..., 2) — money is displayed to 2 decimal places.

Expected output — sample run with P = 10000, R = 8, T = 2, n = 4 (quarterly):

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Q.Write a program that implements a user defined function that accepts Principal Amount, Rate, Time, Number of Times the interest is compounded to calculate and displays compound interest. (Hint: CI=P*(1+r/n)^nt)

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