Problem 5: How long to double your money in a Roth IRA? (20 points) Submit your solution to Gradescope as roth.py You will write a program that calculates the number of months it takes for an investment made in a Roth IRA to double in value. The program will prompt the user for an initial investment amount and an annual percent rate of return (APR). The investment will earn a monthly dividend calculated as 1/12th the APR. The dividend is automatically reinvested each month. No taxes are paid on the investment income. You will use a while loop to implement a monthly calculation and value update. Each month the added interest will be calculated as: added_interest = current_value * (APR / 100) / 12 The loop will terminate as soon as the deposit passes double its initial value. Print out the number of months it took for the initial deposit to double in value at the given rate of return. Here is a short transcript showing how the program would work using an absurd rate of return: Enter an initial Roth IRA deposit amount:1000 Enter an annual percent rate of return:150 Value after month 1: $1125.00 Value after month 2: $1265.62 Value after month 3: $1423.83 Value after month 4: $1601.81 Value after month 5: $1802.03 Value after month 6: $2027.29 It will take 6 months to double your investment with a 150% return