答案和详解如下： LOS d, (Part 2): Calculate and interpret an ordinary annuity and an annuity due. 1、Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is TRUE? A) There is no relationship. B) The present value of the ordinary annuity is equal to annuity due. C) The present value of the ordinary annuity is greater than an annuity due. D) The present value of the ordinary annuity is less than an annuity due. The correct answer was D) With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more. 2、If $2,500 were put into an account at the end of each of the next 10 years earning 15 percent annual interest, how much would be in the account at the end of ten years? A) $27,461. B) $50,759. C) $41,965. D) $79,431. The correct answer was B) n = 10; i = 15; PMT = 2,500 compute FV = $50,759. 3、An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5 percent, what is the present value of the annuity? A) $13,453. B) $23,185. C) $15,000. D) $30,348. The correct answer was C) With Pmt = 5,000, N = 7, I/Y 11.5, value (at t=4) = 23,185.175. Therefore, PV (at t=0) =23,185.175 / (1.115)4 = $15,000.68. 4、An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12 percent, what is the current market value of the bond? A) $950. B) $1,100. C) $1,124. D) $887. The correct answer was D) Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = –886.99. 5、An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream? A) $7,145. B) $6,759. C) $5,759. D) $6,145. The correct answer was B) This is an annuity due problem. There are several ways to solve this problem. Method 1. PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02 Method 2. Put calculator in BGN mode.
N = 10, I = 10, PMT = -1,000 compute PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode. Method 3. You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 * 1.1 = $6,759.02. 6、If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5 percent, how much will an investor have at retirement 45 years from today? A) $100,135. B) $277,700. C) $90,106. D) $901,060. The correct answer was D) N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79 | 
发表于 2008-4-2 12:07
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