42) How much money must you pay into an account at the beginning of each of 20 y

Question

42) How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per year, and round to the nearest $1.
a. $124
b. $111
c. $1,195
d. $139

43) Auto Loans R Them loans you $24,000 for four years to buy a car. The loan must be repaid in 48 equal monthly payments. The annual interest rate on the loan is 9 percent. What is the monthly payment?
a. $500.92
b. $597.24
c. $543.79
d. $563.82
44) If you put $10,000 in an investment that returns 14 percent compounded monthly what would you have after 12 years (round to nearest $10)?
a. $11,490
b. $53,140
c. $48,180
d. $61,270

48) You are considering investing in a project with the following possible out comes:

Probability of Investment States Occurrence Returns
State 1: Economic boom 18% 20%
State 2: Economic growth 42% 16%
State 3: Economic decline 30% 3%
State 4: Depression 10% -25%
Calculate the expected rate of return and standard deviation of returns for this investment, respectively.
a. 2.18%, 1.69%
b. 8.72%, 12.99%
c. 7.35%, 12.99%
d. 3.50%, 1.69%

49) Assume that an investment is forecasted to produce the following returns: a 20% probability of a $1,200 return; a 50% probability of a $5,600 return; and a 30% probability of a $9,500 return. What is the expected amount of return this investment will produce?
a. $7,136
b. $6,125
c. $5,890
d. $4,533


46) You discover an antique in your attic that you purchased at an estate sale 10 years ago for $400. You auction it on EBay and receive $8,000 for your item. What annual rate of return did you earn?
a. 20.00%
b. 34.93%
c. 30.47%
d. 200.00%

Explanation / Answer

42) FV = a*(1+k)*((1+k)^n - 1)/k where FV = 10000 ($) a= annual amount($) at the beginning of each year, k = interest rate = 12% = 0.12, n = 20 years. FV ($)= 10000 = a*1.12*(1.12^20-1)/0.12 = 124 ($) so, OPTION (a) is the ANSWER. 43) PV = 24000 = a*((1+0.09/12)^48 - 1)/(0.09/12 * (1+0.09/12)^48 = 597.24 ($) so, OPTION (b) is the ANSWER. 44) FV= 10000*(1+0.14/12)^12 = 11490 ($) so, OPTION (a) is the ANSWER. 48) expected return (%)= 20*0.18+16*0.42+3*0.3+(-)25*0.1 = 8.72% sd = sqrt((8.72-20)^2 *0.18+(8.72-16)^2 *0.42+(8.72-3)^2 *0.3+(8.72+25)^2 *0.1) = 12.99% so, OPTION (b) is the ANSWER. 49) expected return = 1200*0.20+5600*0.50+9500*0.30 = 5890 ($) so, OPTION (c) is the ANSWER. 46) FV= 8000 = 400*(1+k)^10 where k is annual rate of return => k = 0.3493 = 34.93% so, OPTION (b) is the ANSWER.

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