Problem $6$: How long to double your money $-$ in a Roth IRA? $(15$ points$)$

You will write a program that calculates the number of years 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 yearly dividend which is automatically reinvested. Because it's a Roth, no taxes are paid on the $$nvestment income. You will use a while loop to implement the yearly calculation and value update.

The loop will terminate as soon as the deposit passes double its initial value. Print out the number of years 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 a $15\%$ rate of return:A good place to start would be to look at the compounded$\_$yearly.py program from Unit $4.$