# practice questions

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The incomes of employees for a city are uniformly distributed between \$40,000 and \$50,000. There are a total of 2,500 employees. Approximately how many employees receive wages between \$43,500 and \$46,800?

Select one:

a. 3,300
b. 330
c. 825

SEKHON

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The incomes of employees for a city are uniformly distributed between \$40,000 and \$50,000. There are a total of 2,500 employees. Approximately how many employees receive wages between \$43,500 and \$46,800?

Select one:

a. 3,300
b. 330
c. 825

SEKHON

An investor has \$500,000 to invest at the beginning of the year. The expected return on the portfolio is 11%, the standard deviation 10%, and the riskless rate 5%. At the end of the year, the investor needs \$20,000 for buying a car. Inflation will be 3% during the year. The investor wishes that the real value of the portfolio does not fall during the year. For the real value not be lower than it was at the beginning of the year, the Roy’s Safety First Criterion is:

Select one:

a. 0.20
b. 0.30
c. 0.40

SEKHON

You take a mortgage loan for \$10,000 for 20 years (monthly repayments). The rate of interest is 0.6% per month. If you want to prepay the loan at the end of the 40th month, what is principal left to be repaid? (The monthly payment for the 40th month is not included in the answer.)

Select one:

a. 8,122
b. 9,156
c. 8,835

SEKHON

You invest \$300,000 today at the rate of 10% per year (for the entire length of this investment of \$300,000 from today to year 8). After 5 years from today you invest \$200,000 more at the rate of 12% per year (for the 3 years of this investment of \$200,000 from years 5 to 8). After 8 years from today all your investments are returned to you. How much will you receive after 8 years from today?

Select one:

b. 947,853
c. 924,062
d. 901,055

SEKHON

mohitester wrote:

The incomes of employees for a city are uniformly distributed between \$40,000 and \$50,000. There are a total of 2,500 employees. Approximately how many employees receive wages between \$43,500 and \$46,800?

Select one:

a. 3,300
b. 330
c. 825

Let X be the amount of wages employees received.

Since it is uniformly distributed,
P[43500 = (46800-43500)/(50000-40000)
=3300/10000
=.33

E[X]= .33 * 2500 = 833

Execuse me. Have you read through the materials yet?

Barring the last line typo, EddieChen is right.

The relevant concept is the probability mass function. You first find the proportion of observations that lies between 43.5 and 46.8k, and then multiply that by 2500 to answer the question.

mohitester wrote:

You invest \$300,000 today at the rate of 10% per year (for the entire length of this investment of \$300,000 from today to year 8). After 5 years from today you invest \$200,000 more at the rate of 12% per year (for the 3 years of this investment of \$200,000 from years 5 to 8). After 8 years from today all your investments are returned to you. How much will you receive after 8 years from today?

Select one:

b. 947,853
c. 924,062
d. 901,055

Worry only about the future values. Draw a timeline if you should.

300k * 1.1^8=643.08

200k * 1.12^3=280.99

Sum: 924.06k

mohitester wrote:

You take a mortgage loan for \$10,000 for 20 years (monthly repayments). The rate of interest is 0.6% per month. If you want to prepay the loan at the end of the 40th month, what is principal left to be repaid? (The monthly payment for the 40th month is not included in the answer.)

Select one:

a. 8,122
b. 9,156
c. 8,835

At onset, you borrow 10k, so PV=10, 000. FV=0, i=0.6, n=240 months. PMT should be in 78.7. If you want to prepay at the end of the fortieth month, you need to pay the present value of the loan at that point. End of period 40, means you have 200 periods to go. So set, n=200, and PV should give you the answer.

mohitester wrote:

An investor has \$500,000 to invest at the beginning of the year. The expected return on the portfolio is 11%, the standard deviation 10%, and the riskless rate 5%. At the end of the year, the investor needs \$20,000 for buying a car. Inflation will be 3% during the year. The investor wishes that the real value of the portfolio does not fall during the year. For the real value not be lower than it was at the beginning of the year, the Roy’s Safety First Criterion is:

Select one:

a. 0.20
b. 0.30
c. 0.40

For the real value of the portfolio not to fall during the year, the investor needs to make 0.03 * 500k = 15k just to keep up with inflation, and an extra 20k for buying the car. That implies an income of 35k from the portfolio over the course of the year, or equivalently a 7% return. Roy’s Criterion is like the Sharpe exept it uses this minimum required return instead of the riskless rate (note that the latter is thrown in to trick you). Thus, RSFC = (0.11 - 0.07) / 0.1 = 0.4.