Using the Design Recipe, write the algorithm (not the program) for the following problems:

• Write a program that prints the sum of the first n positive integers, 1 + 2 + … + n, where n is user-specified.
• Write a program that prints the product of the first n positive integers, 1 × 2 × … × n, where n is user-specified.
• Write a program that prints the balance of an account after each of a number of years y, given an initial balance b and a yearly interest i, specified as a percentage (e.g., 5%). The values of y, b and i are all user-specified.

Make sure, for each problem, you clearly show the Design Recipe steps:

1. Contract (25%)
2. Purpose Statement (25%)
3. Examples (25%)
4. Algoritm (25%)