Question
A savings account typically accrues savings using compound interest. If you deposit $1000 with a 10% interest rate per year, after one year you will have $1100. If you leave this money in the account for another year at 10% interest, you will have $1210. After three years you will have $1331, and so on.
Write a program that inputs the initial amount, an interest rate per year, and the number of years the money will accrue compound interest. Write a recursive function that calculates the amount of money that will be in the savings account using the input information.
To verify your function, the amount should be equal to P(1+i)n, where P is the amount initially saved, i is the interest rate per year, and n is the number of years.
Answer
PROGRAM CODE:
//Header section
#include <iostream>
#include <cmath>
using namespace std;
// Recursive function to calculate the amount with compound interest
double calculateCompoundInterest(double initial_amount, double interest_rate, int num_years)
{
// Base case: if no years left, return the initial amount
if (num_years == 0)
{
return initial_amount;
}
// Recursive case: calculate the amount after one year with compound interest
double amount_after_one_year = initial_amount * (1 + interest_rate);
// Recur for (num_years - 1) to calculate the amount after the remaining years
return calculateCompoundInterest(amount_after_one_year, interest_rate, num_years - 1);
}
int main()
{
//Declare variables
double initial_amount, interest_rate;
int num_years;
// Input the initial amount, interest rate, and number of years
cout << "Enter the initial amount: $";
cin >> initial_amount;
cout << "Enter the interest rate per year (in decimal): ";
cin >> interest_rate;
cout << "Enter the number of years: ";
cin >> num_years;
// Calculate the amount using the recursive function
double amount = calculateCompoundInterest(initial_amount, interest_rate, num_years);
// Output the result
cout << "The amount after " << num_years << " years is: $" << amount << endl;
return 0;
}
OUTPUT:
Enter the initial amount: $50000
Enter the interest rate per year (in decimal): 2
Enter the number of years: 10
The amount after 10 years is: $2.95245e+09