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])

Because growthRates is a sequence (you’re even iterating it!) and you multiply it by (1 + 0.01), which is obviously a float (1.01). I guess you mean for growthRate in growthRates: ... * growthrate?

In this line:

fund = fund * (1 + 0.01 * growthRates) + depositPerYear

I think you mean this:

fund = fund * (1 + 0.01 * i) + depositPerYear

When you try to multiply a float by growthRates (which is a list), you get that error.

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'

In this line:

fund = fund * (1 + 0.01 * growthRates) + depositPerYear

growthRates is a sequence ([3,4,5,0,3]). You can’t multiply that sequence by a float (0.1). It looks like what you wanted to put there was i.

Incidentally, i is not a great name for that variable. Consider something more descriptive, like growthRate or rate.