7.1

Effective interest is calculated straight from the formula, if you know the formula you just sub the given interest and its compounding period as in the board bellow

7.2

In this case we have an asset that is said to depreciate, decay formula should be used. It will be compound decay since it’s diminishing balance. And we just have to substitute, no further thinking.

7.3.1

2 years after the investment she will have the initial amount plus interest, the interest change is from year 3 onwards. So we will compute the initial amount and interest only, compounded quarterly

7.3.2

After 7 years we will have to integrate the change of interest by multiplying with a second factor bracket of 7.8% compounded monthly for 5 years, the initial amount will have the original factor bracket upto two years.

Then we subtract the withdrawal and interest that it would have earned for the 3 years that it was robbed of. When she takes 2500 at year four instead of year seven, she robs herself of the interest she would have earned had she not withdrew the amount

Check the answer on the board below

Now let’s do one more question:

9.1

Two events are independent if the probability of the intersection is equal to the product of probabilities of those events.

So, we have to compute the probability of intersection and of each event, if the above rule is satisfied, then the events will be independent.

Check answer on the board

9.2.1

For events to be mutually exclusive, they cannot happen at the same time, that means the probability of their intersection has to be zero. In this case, it is not. The events are not mutually exclusive

9.2.2

We are given everything to satisfy the addition rule and replace probability of B with 4xP(A), from here we have one variable and we can solve for probability of A, then multiply by four to get the probability of B as required.

9.2.3

Probability not A is everything else that is not in event A, the sum of all probabilities will always add upto 1.

So, we can simply say 1 minus probability of A to get all events outside event A

Answer: