You have a lot of questions. I hope this helps and that I have interpreted your questions correctly. Please note that I am not familiar with business economics. My answers are based on the math and a small amount of research, so they may not be correct.
Simple interest is I=PTR/100 where P is the principal amount, R the annual percentage rate and T the time in years. The amount A after T years is P+I=P(1+TR/100).
1. Amount after 5 years=200(1+5*4/100)=200*1.2=$240. In other words, 200+40 dollars.
2. For each separate investment of $200 you get $8 each year in interest (because 200*1*4/100=8) so that at the end of the year you have $208. So in 5 years when you add together all your investments you end up with 5*208=$1040. In other words, you invested $1000 altogether, and you got $8 interest for each year, making the total interest 5*8=$40. 1000+40=$1040.
3. I interpret this as saying that a principal amount P will amount to $30000 in 10 years' time. R=10% and T=10, so A=P+I=30000=P(1+10*10/100)=2P so 2P=$30000 and P=$15000. In today's money $15000 will grow to $30000 in 10 years.
4. If $3000 is invested for a year, I=3000*10/100=$300. In the first year, $3000 grows to 3000+300=$3300. If this amount is not re-invested, in the second year $3000 will also grow to $3300, and so on. In 10 years the total amount will be 3300*10=$33000. [The answer is different and more complicated if in the second year, $3300 (earned from the first year) is invested together with another $3000, making $6300 as the second year's investment. Another 10% interest is now earned on $6300, making 6300+630=$6930 to be added to another $3000 making $9930 as the amount invested for the third year. And so on. Quite complicated!]
5. The facts about how the $300 is obtained are not relevant. The only important fact is that you started with $300, and invested $100 at 3%, earning I=100*1*3/100=$3. The amount after 1 year from the invested money is 100+3=$103. Add this to the hidden $200 to make $303.
6. Offer 1: $4000000 makes 4000000*10/100=$400000 interest and the total amount becomes $4400000. This happens every year for 5 years, so 5*4400000=$22000000 or $22 million.
Offer 2: $2000000 a year raises $200000 in interest making $2200000 each year for 5 years=$11 million. We add that to the lump sum of $8 million making $19 million. So offer 1 is better.
7. A company's planning process to decide on the best investments to make.
8. Payback Method ignores what real value the money returned has at the time it is returned. It is disadvantageous to opt for a longer rather than a shorter period when planning investments.
9. NPV rule: reject investment if NPV negative; accept if positive.
10. Initially there is no cash inflow because the show has not yet run. The current assets are zero, NPV=0. But since this is not negative, the investment should be accepted. The expected returns are $20M plus annual interest=5000000*7/100=$350000 per year for four years=$1400000. Total expected amount after 4 years is 20000000+1400000=$21400000 which exceeds the initial cost of production. The investment would appear to be justified.
I hope I've been of some help.