D) Ahmad invested 12,000 at 12 to his 3 children when they rea 4000 ar 12%...

The initial principal amount invested is $12,000 which is to be compounded on a monthly basis. Thereafter, each son would get the same amount when they turn 20. Their age at the time of making the investment is 18, 16 and 14. This means that the amount would be withdrawn at a gap of every two years.

For the sake of computation, let's presume that the equal amount to be withdrawn by the sons be 'x'.

After the expiry of two years, the value of the investment would be computed as follows:-

= P (1+i)^n   {where P = Principal amount invested; i = equated rate of interest for each compounding period and

n = number of times compounding is done}

= 12000(1 + 12%/12) ^12*2

= 12000(1 + 0.01)^24

= 12000 * 1.2697

=$ 15236.40

Now, the eldest son is 20 years old and he would receive an amount of x. Therefore, the remaining amount would be $(15236.40 - x). This amount would be compounded for the next two years which would become:-

=(15236.40 - x) * (1.01)^24

=(15236.40 - x) * 1.2697

=19345.66 -1.2697x

Now the middle sibling would be 20 years old and therefore x amount would be withdrawn again from the investment which would become

19345.66 -1.2697x - x = 19345.66 - 2.2697x

Now the remaining amount would remain invested for the next two years and then after compounding it should be equal to x.

(19345.66 - 2.2697x) * (1.01)^24 = x

(19345.66 - 2.2697x) * 1.2697 = x

24563.18 - 2.8818x = x

3.8818x = 24563.18

x = 24563.18/ 3.8818

x = 6327.78

Therefore, the amount that each son would get is $6327.78.

I hope it was explained well. In case you have any queries, please comment so that I would be able to clear it. I would be more than please to further help on this question in case of any such requirement.