Purchase on credit#394
The bank offers a loan for purchasing a product with the following terms. If you buy a product worth on credit for months, your initial payment will be . This is followed by monthly payments of for the next N - 1 months. At the end of the months, you must pay the accumulated interest for using the credit, which is calculated as follows:
For the first month, the interest is P \cdot (N - 1) \cdot S / N.
For the second month, the interest is calculated on the remaining unpaid value of the product as P \cdot (N - 2) \cdot S / N, plus interest on the previous month's interest, which is P \cdot P \cdot (N - 1) \cdot S / N.
This pattern continues for each subsequent month.
Write a program to calculate the amount of the final payment.
The first line of the input contains three numbers separated by spaces: the purchase price (an integer, 0 < S < 10^9), the number of months (an integer, 0 < N < 100), and the interest rate (a real number, 0 < P \leq 0.01).
Output the amount of the final payment, rounded to a precision of 10^{-2}.
Example 1