can't multiply sequence by non-int of type 'float'

for i in growthRates:  
    fund = fund * (1 + 0.01 * growthRates) + depositPerYear

should be:

for i in growthRates:  
    fund = fund * (1 + 0.01 * i) + depositPerYear

You are multiplying 0.01 with the growthRates list object. Multiplying a list by an integer is valid (it's overloaded syntactic sugar that allows you to create an extended a list with copies of its element references).

Example:

>>> 2 * [1,2]
[1, 2, 1, 2]

Python allows for you to multiply sequences to repeat their values. Here is a visual example:

>>> [1] * 5
[1, 1, 1, 1, 1]

But it does not allow you to do it with floating point numbers:

>>> [1] * 5.1
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't multiply sequence by non-int of type 'float'

You're multipling your "1 + 0.01" times the growthRate list, not the item in the list you're iterating through. I've renamed i to rate and using that instead. See the updated code below:

def nestEgVariable(salary, save, growthRates):
    SavingsRecord = []
    fund = 0
    depositPerYear = salary * save * 0.01
    #    V-- rate is a clearer name than i here, since you're iterating through the rates contained in the growthRates list
    for rate in growthRates:  
        #                           V-- Use the `rate` item in the growthRate list you're iterating through rather than multiplying by the `growthRate` list itself.
        fund = fund * (1 + 0.01 * rate) + depositPerYear
        SavingsRecord += [fund,]
    return SavingsRecord 


print nestEgVariable(10000,10,[3,4,5,0,3])