Ralph will retire 15 years from today and has saved $121,000 in his investment account for
retirement. He believes he will need 37,000 at the beginning of each year for 25 Years of re-
tirement, with the first withdrawal on the day he retires. Ralph assumes his account will earn
8%. The amount he needs to deposit at the beginning of this year and each of the following
14 Years (15 in all) is closest to:
a) 1350
b) 1450
c) 1550
ANSWER
B = 1450
Step 1:
Calculate the amount needed at retirement at t = 15, with your calculator in BGN mode.
N = 25, FV = 0, I/Y = 8, PMT = 37,000, CPT PV = -426,564
Step 2:
Calculate the required deposits at t = 0,1,....,14 to result in a time 15 value of 426,564, with
your calculator still in BGN mode.
PV = -121,000, N = 15, I/Y = 8, FV = 426,564, CPT PMT = -$1,457.21
Colonia has 2 political parties, the Wigs and the Wags. If the Wags are elected there is a 32%
probability of a tax increase over the next 4 years. If the Wigs are elected there is a 60%
probability of a tax increase. There is a 20% probability the that the Wags will be elected.
The sum of the (unconditional) probability of a tax increase and the joint probability that the
wigs will be elected and there will be no tax increase is closest to:
a) 55%
1
,b) 70%
c) 85%
ANSWER
86.4% = C
The unconditional probability of a tax increase is: 0.2(0.32) + 0.8(0.6) = 54.4%.
The joint probability that the Wigs will be elected and there will be no tax increase is:
0.8(0.4) = 32%. The sum is: 54.4 + 32 = 86.4%.
Allen Jabber invested $400 at the beginning of the last 12 months in the shares of a mutual
fund that paid no dividends. Which Method will he correctly choose to calculate his average
price per share from the monthly share prices?
a) Arithmetic Mean
b) Harmonic Mean
c) Geometric Mean
ANSWER
Harmonic Mean - The harmonic mean of the 12 purchase prices will be his average price
paid per share.
An analyst who wants to display the relationship between two variables graphically is most
likely to use:
a) a histogram
b) a scatterplot
c) a frequency polygon
ANSWER
B = Scatterplot
2
, Scatterplots illustrate the relationship between two variables.
Histograms and frequency polygons show the distribution of observations for a single varia-
ble.
The current price of Bosto shares is $50. Over the coming year, there is a 40% probability
that share returns will be 10%, 40% probability returns will be 12.5%, and a 20% probability
share returns will be 30%. Bostos expected return and standard deviation of returns for the
coming year are closest to:
a) E(R) = 15% Standard Dev = 7.58%
b) E(R) = 17.5% Standard Dev = 5.75%
a) E(R) = 17.5% Standard Dev = 7.58%
ANSWER
A
E[R] = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%
Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
Standard deviation=√57.5=7.58%
Nikki Ali and Donald Ankard borrowed $15,000 to finance their wedding and reception. The
fully amortizing loan at 11% requires equal payments at the end of each of the next seven
years. The principle portion of the first payment is closest to:
A) 1500
B) 1530
C) 1560
ANSWER
B
3
retirement. He believes he will need 37,000 at the beginning of each year for 25 Years of re-
tirement, with the first withdrawal on the day he retires. Ralph assumes his account will earn
8%. The amount he needs to deposit at the beginning of this year and each of the following
14 Years (15 in all) is closest to:
a) 1350
b) 1450
c) 1550
ANSWER
B = 1450
Step 1:
Calculate the amount needed at retirement at t = 15, with your calculator in BGN mode.
N = 25, FV = 0, I/Y = 8, PMT = 37,000, CPT PV = -426,564
Step 2:
Calculate the required deposits at t = 0,1,....,14 to result in a time 15 value of 426,564, with
your calculator still in BGN mode.
PV = -121,000, N = 15, I/Y = 8, FV = 426,564, CPT PMT = -$1,457.21
Colonia has 2 political parties, the Wigs and the Wags. If the Wags are elected there is a 32%
probability of a tax increase over the next 4 years. If the Wigs are elected there is a 60%
probability of a tax increase. There is a 20% probability the that the Wags will be elected.
The sum of the (unconditional) probability of a tax increase and the joint probability that the
wigs will be elected and there will be no tax increase is closest to:
a) 55%
1
,b) 70%
c) 85%
ANSWER
86.4% = C
The unconditional probability of a tax increase is: 0.2(0.32) + 0.8(0.6) = 54.4%.
The joint probability that the Wigs will be elected and there will be no tax increase is:
0.8(0.4) = 32%. The sum is: 54.4 + 32 = 86.4%.
Allen Jabber invested $400 at the beginning of the last 12 months in the shares of a mutual
fund that paid no dividends. Which Method will he correctly choose to calculate his average
price per share from the monthly share prices?
a) Arithmetic Mean
b) Harmonic Mean
c) Geometric Mean
ANSWER
Harmonic Mean - The harmonic mean of the 12 purchase prices will be his average price
paid per share.
An analyst who wants to display the relationship between two variables graphically is most
likely to use:
a) a histogram
b) a scatterplot
c) a frequency polygon
ANSWER
B = Scatterplot
2
, Scatterplots illustrate the relationship between two variables.
Histograms and frequency polygons show the distribution of observations for a single varia-
ble.
The current price of Bosto shares is $50. Over the coming year, there is a 40% probability
that share returns will be 10%, 40% probability returns will be 12.5%, and a 20% probability
share returns will be 30%. Bostos expected return and standard deviation of returns for the
coming year are closest to:
a) E(R) = 15% Standard Dev = 7.58%
b) E(R) = 17.5% Standard Dev = 5.75%
a) E(R) = 17.5% Standard Dev = 7.58%
ANSWER
A
E[R] = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%
Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
Standard deviation=√57.5=7.58%
Nikki Ali and Donald Ankard borrowed $15,000 to finance their wedding and reception. The
fully amortizing loan at 11% requires equal payments at the end of each of the next seven
years. The principle portion of the first payment is closest to:
A) 1500
B) 1530
C) 1560
ANSWER
B
3
