Human capital for under developed countries
If you multiply the index by the population size (or the quantity used to compute the per person index), you get an index of the stock of human capital. For example, if for a given country the index is $h_t$ and population is $N_t$, then the stock is:

$$ H_t = h_t \times N_t $$

Now, by the definition a stock follows an accumulation rule, just as physical capital:

$$ H_{t+1} = H_t(1+d_t) + I_t $$

where $d_t$ is the "depreciation" of HK (e.g. because of death or skill obsolescence) and $I_t$ is gross investment in HK. Since you probably do not have data on depreciation (which I imagine is very difficult to compute), you can only calculate net investment, which is equivalent to net savings by definition:

$$ S^h_t = H_{t+1} - H_t $$

Finally, to compute the savings rate, you need to divide this by a measure of GDP. However, these need to be measured in the same units. Therefore, you need to transform $H_t$ or $S^h_t$ into monetary units. For this you need something like the average price of human capital for every period, which I have never seen, and seems not available in Penn-world tables.