117. sami opens an account and deposits $100 into it at the end of each month. the account earns 2% per year compounded monthly. let sn denote the amount of money in her account at the end of n months (just after she makes a deposit). for example, s1 = 100 and s2 = 100(1 + 0.02 /12)+100
c. find an explicit function for sn, and use it to find s12.

The explicit function is:

where

and we calculate S12:

Step-by-step explanation:

Expanding a few steps of the compound interest:

We can write:

for deposits

Then, expanding the previous equations would yield:

This is a geometric series form, which can be simplified to:

plugin in the values for the 12 month gives:

step-by-step explanation:

70

step-by-step explanation: