A few questions actually. How do you do 13.8 * 1.05^5 ? Do you do this for each year? 13.8 * 1.05 = 14.49 * 1.05 = 15.21 * 1.05 = 15.97? And so on? This seems very time consuming, even for the PST. Doing this for 10 years would be even more time consuming. And I also don't really understand the second part of the explanation, can you please rephrase it?

(edited)

Paul, there are two shortcuts that might help you in some of these problems (but I don't believe any of them would be particular useful in this particular example). First, for small annual growth rate values and short period of times, you can get a ballpark estimate by linearly multiplying the growth rate by the number of years (in this case 5 * 5% = 25%, which will give 13.8 * 1.25 = 17.25; quite near the absolute value of 17.6). Second, you could use the rule of 72, which tells you that a number will take 72/growth rate to double up (at a 5% growth rate, the initial number will double in approximately 14.4 years).

(edited)

Regarding the second part of the explanation, you will need to do an iterative process of elimination. 3.3 * 1.15 ^5 = 6.63, so less than half of the other type of capital (17.6). Repeat the same for 20% and still less, so it will only work for 25% (3.3 * 1.25 ^5 = 10.08). In this case, using the proxy method I described before would give you a wrong answer, because the numbers are all very similar

I understand how to answer this question. Essentially you calculate the growth of Innovation Capital over 10 years at a 5% interest rate, and then see how much Human capital needs to grow to comprise 50% of that found figure. I guess my problem is that calculation 1.05*1.05*1.05.... ten times, seems so time consuming. And if shortcuts don't really work, how else to approach it?

How 1.05 came