**C programs to calculate compound interest** have been shown here. Both of the iterative and recursive approaches have been covered. Compound interest can also be calculated using formula:

$CI = {\Large p*(1 + \frac{r}{n})^{nt} - p}$

Here $CI$ represents compound interest. Pricipal amount, interest rate, periodicity of payment and time in years have been represented by $p$, $r$, $n$ and $t$ respectively. As an example, If $p = 5000$, $r = 7.5$ , $n = 4$ and $t = 2$ then by using the above formula, we get the value of compound interest $CI = 801.11$.

The following section covers the C programs to calculate compound interest along with algorithm, pseudocode and time complexity of the program.

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**5. Program: Iterative approach**

**6. Program: Recursive approach**

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## 1. Algorithm to calculate compound interest

1. Take input of Pricipal amount ($p$), interest rate ($r$), payment periodicity ($n$) and years ($t$)

2. Calculate compound interest using formula $CI = p*(1 + \frac{r}{n})^{nt} - p$

3. Return the computed value $CI$

## 2. Pseudocode to calculate compound interest

**Input**: Pricipal $p$, interest rate $r$, payment periodicity $n$, time in years $t$

**Output**: Compound interest $ci$

1. **Procedure** compoundInterest($p$, $r$, $n$, $t$):

2.

3. **Return** $ci$

4. **End Procedure**

## 3. Time complexity to calculate compound interest

**Time Complexity: ****O(nt)**

Here $t$ is the no. of years and $n$ is the payment periodicity.

## 4. C Program & output to calculate compound interest using formula

/******************************* alphabetacoder.com C program to calculate compound interest using formula ********************************/ #include <stdio.h> #include <math.h> int main() { // declare variables float ci, amount, p, r, t; int n; // take input of initial principal amount, // interest rate, periodicity of payment and year printf("Enter the principal balance = "); scanf("%f", & p); printf("Enter the annual interest rate = "); scanf("%f", & r); printf("Enter compound frequency / year = "); scanf("%d", & n); printf("Enter the year = "); scanf("%f", & t); // calculate compounded value // using formula amount = p * pow((1 + r / (100 * n)), n * t); //find the compound interest ci = amount - p; // display result rounded up to two decimal places printf("Compound interest = %0.2f", ci); return 0; }

Output

Enter the principal balance = 20000

Enter the annual interest rate = 8

Enter compound frequency / year = 4

Enter the year = 10

Compound interest = 24160.76

## 5. C Program & output to calculate compound interest using Iteration

/******************************* alphabetacoder.com C program to calculate compound interest using Iteration *********************************/ #include <stdio.h> int main() { // declare variables float ci, amount, p, r, t; int n, i; // take input of initial principal amount, // interest rate, periodicity of payment and year printf("Enter the principal balance = "); scanf("%f", & p); printf("Enter the annual interest rate = "); scanf("%f", & r); printf("Enter compound frequency / year = "); scanf("%d", & n); printf("Enter the year = "); scanf("%f", & t); // initialize amount = p; // calculate compounded value using loop for (i = 0; i < n * t; i++) amount = amount + amount * (r / (n * 100)); //find the compound interest ci = amount - p; // display result rounded up to two decimal places printf("Compound interest = %0.2f", ci); return 0; }

Output

Enter the principal balance = 33000

Enter the annual interest rate = 8.25

Enter compound frequency / year = 2

Enter the year = 10

Compound interest = 41065.21

## 6. C Program & output to calculate compound interest using recursion

/******************************* alphabetacoder.com C program to calculate compound interest using recursion ********************************/ #include <stdio.h> // recursive function to compute compound interest float compound_interest(float p0, float p, float r, int n, int t, int itr) { // if number of total no of compound reached if (itr == n * t) return (p - p0); // calculate interest float interest = p * (r / (n * 100)); // call function return compound_interest(p0, p + interest, r, n, t, itr + 1); } int main() { // declare variables float ci, p, r; int n, i, t; // take input of initial principal amount, // interest rate, periodicity of payment and year printf("Enter the principal balance = "); scanf("%f", & p); printf("Enter the annual interest rate = "); scanf("%f", & r); printf("Enter compound frequency / year = "); scanf("%d", & n); printf("Enter the year = "); scanf("%d", & t); // call function to compute compound interest ci = compound_interest(p, p, r, n, t, 0); // display result rounded up to two decimal places printf("Compound interest = %0.2f", ci); return 0; }

Output

Enter the principal balance = 33000

Enter the annual interest rate = 8.25

Enter compound frequency / year = 2

Enter the year = 10

Compound interest = 41065.21

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