Sophie deposited money into an account in which interest is compounded semi-annually at a rate of 3.2%. she made no other deposits or withdrawals and the total amount in the account after 7 years was $13,987.17. how much did she deposit?

For this we are going to work backwards. We also use an exponent of 14 since the money was invested for 7 years and compounded twice a year (14 times).

13,987.17 = X (1+.032)^14          (divide both sides by (1.032)^14 )
13,987.17 / (1.032)^14 = X (amount deposited)
8999.41 = X