Can someone give me a hand with understanding how the $640,000 and $695,000 figures are derived in the below example?

Even in jurisdictions with relatively small annual exclusions, a gifting program that is started early and implemented over long periods of time can transfer substantial wealth in a tax-efficient manner. In the United States, for example, a donor’s annual gift exclusions are currently limited to US$13,000 per year (for 2009), per donee (e.g., a parent may annually transfer US$13,000 to each child or US$26,000 from both par- ents). Exhibit 4 shows that an annual gifting program of transferring US$13,000 per year tax free implemented over a 30-year period transfers over **US$640,000** inflation- adjusted dollars at an 8 percent nominal return that is taxed at 25 percent annually with a 2.5 percent inflation rate (i.e., 5.5 percent real rate of return).19 The dashed line in Exhibit 4 represents the accumulated value of the gifts themselves, excluding investment returns. After 30 years, gifts total US$390,000 = US$13,000 × 30. If the donor had kept this amount, any future appreciation would have increased the value in his estate and hence the estate tax liability. Assuming an 8 percent nominal pretax return that is subject to a 25 percent annual tax would add an additional US$305,000 of real appreciation (after adjusting for inflation), for a total value of **US$695,000**. A tax-efficient investment strategy that defers the 25 percent tax until the end of the investment horizon increases the accumulated sum to almost US$843,000.

For the ‘over $640,000’ figure I used the after tax nominal return of 6% and adjusted it to 3.4% after tax real return, by 1.06/1.025 and the FV of a 30 year $13,000 payment stream gives me $660,158 but I’m not sure if this is even what they’re getting at. As for the $695,000, clueless.

Thanks!