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The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

A.

1.50%

B.

6%

C.

6.14%

D.

None of the above

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

A.

1 048 574

B.

1 048 595

C.

2 097 170

D.

2 097 172

Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A.

F(x)G(x)

B.

F(x)g(x) + f(x)G(x)

C.

F(x)g(x) - ∫F(x)g'(x)dx

D.

f(x)G(x) - ∫F(x)g'(x)dx

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

A.

16%

B.

17.4%

C.

20%

D.

24.4%

The fundamental theorem of analysis establishes a relation between

A.

First and second derivative of a function

B.

The derivative of a function and the slope of its graph

C.

Integration and differentiation of functions

D.

The derivative of a function and the derivative of its inverse function

For the function f(x) =3x-x3 which of the following is true?

A.

x = 0 is a minimum

B.

x = -3 is a maximum

C.

x = 2 is a maximum

D.

None of these

A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A.

0.7367

B.

0.3483

C.

0.2646

D.

None of these

What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

A.

x ln(x) - x

B.

ln(x) - x

C.

1/x

D.

exp(x)

Which of the following statements is true for symmetric positive definite matrices?

A.

Its eigenvalues are all positive

B.

One of its eigenvalues equals 0

C.

If a is its eigenvalue, then -a is also its eigenvalue

D.

If a is its eigenvalue, then is also its eigenvalue