econ maths questions. help pls.. from genius?

Question

1. a sum of £10,000 is invested at 6% for one year. Determine the value at the end of year if interest is compouned.
2.1 quarterly (every 3 months)
2.2 monthly
2.3 Weekly




2. a sum of £150 is placed at the beginning of each month in an account with an annual interest rate of 6%, compounded monthly. How much money is there in the account at the end of the first year?(clarification: at the end of the first year’ means that 12 payments have been made. The 13th payment has not been made yet)

3. you have just won £ 4000,000 in the lottery, in order to collect the money. You must choose one of the following two options: a) the whole amount right now, or b) 500,000 a year for ten years. The first payment starting exactly one year from now, assuming that annual interest rates r 5% and compounded annually, which option is best? Use the concept of present value to estimate how much option b) is worth to you right now.

4. a monopolist faces a demand function D(p) = √1-P², where p is price,
5.1 calculate the marginal revenue as a function of price. Then find the price that maximises revenue.


5.2 suppose that price is increased from p=0.1 to p=0.2, by how much does revenue change? Compare your answer with an estimate based on a linear approximation of the revenue function at p=0.1


5, for each of the following functions, find and classify the critical points. And the global maxima and minima if they exist, then sketch the function.
6.1 f(x)= x³ -18x² +33x +150. with X>=0;
6.2 g(x) = x³-18x²+33x + 150 0<=x<=12;
6.3 h(x) =(a²-x²)3/2. with –a<=x<=a and a a given real number

Answer 1

To increase by 6% compounded annually for N years, multiply by 1.06^N.

If compounding is quarterly, multiply by 1.015^(4N).

If compounding is monthly, multiply by 1.005^(12N).

This is because 6% = .06, 6%/4 = .015, and 6%/12 = .005

Beyond that, you asked way too many disparate problems in a single post. Please re-ask them separately if you still need help.