Quiz Chapter 5
93. To pay for her college education, Gina is saving $20,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year?
$275,520 FVAD = PMT x [FVOAIF12%, 8 x (1.12)] = 20,000(12.3) (1.12) = 275,520
89. The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is
$31,292 FVAD = PMT x [FVOAIF8%, 10 x (1.10)] = 2,000(14.487)(1.08) = 31,292
88. Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year?
$31,874 FVOA = PMT x [FVOAIF10%, 10] = 2,000(15.937) = 31,874
83. Under MACRS, an asset which originally cost $100,000, incurred installation costs of $10,000, and has an estimated salvage value of $25,000, is being depreciated using a 5 year normal recovery period. The cost of the asset that has yet to be depreciated at the end of year 1 is
$88,000 = Original cost + installation cost - accumulated depreciation = [100,000 +10,000] - [(100,000 +10,000)*.2] = 88,000; No salvage value is considered under MACRS
95. The rate of interest actually paid or earned annually is called the ______ interest rate.
effective
90. The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is
$11,464 FVOA = PMT x [FVOAIF3%, 10] = 1,000(11.464) = 11,464
94. Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 17 percent on its investments. Year Amount 1 $3,000 2 6,000 3 9,000
$20,127 > F = 3,000 (1.17)2 + 6,000(1.17) + 9,000 = 20,127
96. The future value of $200 received today and deposited at 8 percent compounded semi annually for three years is
$253 F = 200 (1.04)6 = 253; note that the annual interest is divided by 2 and there are 6 semiannual periods in 3 years.
85. To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year?
$27,552 FVAD = PMT x [FVOAIF12%, 8 x (1.12)] = 2,000(12.3) (1.12) = 27,552
87. The present value of a $20,000 perpetuity at a 7 percent discount rate is
$285,714 Present value of a perpetuity (PVP) = Annuity/ discount rate = 20,000/.07 = $285,714
92. A generous benefactor to the local ballet plans to make a one time endowment which would provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be?
$3,000,000 PVP = 150,000/.05 = 3,000,000
97. The rate of return (r) earned on an investment of $50,000 today that guarantees a perpetual income of $10,489 per year is approximately
21% > PVP = 50,000 = 10,489/r, solve for r and get 21%
82. Indicate which of the following is true about annuities.
An annuity due is an equal payment paid or received at the beginning of each period.
86. Indicate which of the following is true about annuities.
An annuity due is an equal payment paid or received at the beginning of each period.
84. Indicate which formula is correct to determine the future value of an annuity due.
FVADs = PMT x [FVIFAi,n x (1 + i)]
91. If the present value of a perpetual income stream is increasing, the discount rate must be
decreasing
