I was asked to calculate the implicit interest rate in a finance lease. The leasing arrangement (lease term is 5 years) comprises of lease payments being made semiannually (i.e. 1 July and 1 Jan – lease begins on 1 Jan and payments start on 1 July of that year and thereafter) and an unguaranteed residual, do I use an annuity rate for 10 periods to calculate the PV of the 10 lease payments and a discount rate for a single amount for 10 periods to calculate the PV of the unguaranteed residual? If so, will I use the same implicit interest rate to calculate the interest expense and principal reduction (lease liability) amount for the first payment on 1 July in the books of the lessee?

You're certainly on the right track, Steve. You will determine the PV of the 10 semiann lease payments, and the PV of the single residual amount, using the same discount rate. But, you'll need to find a discount rate so that this PV sum is equal to the fair value of the asset as of the lease's inception. You didn't mention the asset's FV, but it's given somewhere in your background info.

Having done so, you'll then proceed as you're thinking... use that rate to "amortize" the implied liability, with each lease payment consisting of an interest expense element, and a principal-reduction element.