Using Table 12A.1 and Table 12A.2 of this chapter, determine the answers to each

Question

Using Table 12A.1 and Table 12A.2 of this chapter, determine the answers to each of the following independent situations. (Round answers to the nearest whole number.)

(a) The future value in three years of $2,000 deposited today in a savings account with interest compounded annually at 4 percent.

(b) The present value of $9,000 to be received in six years, discounted at 12 percent.
(c) The present value of an annuity of $5,000 per year for seven years discounted at 18 percent.

(d) An initial investment of $42,680 is to be returned in eight equal annual payments. Determine the amount of each payment if the interest rate is 10 percent.

(e) A proposed investment will provide cash flows of $30,000, $9,000, and $6,000 at the end of Years 1, 2, and 3, respectively. Using a discount rate of 14 percent, determine the present value of these cash flows.
Year 1 $ Answer
Year 2 $ Answer
Year 3 $ Answer

(f) Find the present value of an investment that will pay $9,000 at the end of Years 10, 11, and 12. Use a discount rate of 12 percent.

Explanation / Answer

1 A = P ( 1 + r/n ) nt, with P = 2000, r = 4/100 = 0.04, n = 1, t = 3. Therefore, A = 2000(1+.04/1)^1*3 =2000(1.04)^3 =2000(1.04)^3 = $2250 2 PV = FV / (1+r)n FV is Future Value = $6000. r is the interest rate = 0.12 (as a decimal, so 0.10, not 10%) n= 6 yr PV = $6000/(1+.10)^6 =$6000*0.5645 =$3387 3 where C = Cash flow per period i = interest rate n = number of payments FV = $ 5000*[(1-(1+0.18)^-7)/0.18]*(1+0.18) =$5000*[(1-0.313925)/0.18]*1.18 =$5000*[0.686075/0.18]*1.18 =$5000*[3.811528*1.18] =22488$ $ 4 Annual Installlment = initial investment/sum of PVF of 10% for 8 yrs = $42680/5.3349 = $8000 8000.14996 5 Year PVF @14% Amount PV(PFV*Amt) 1                           0.88 $30,000 $26,315.79 2                           0.77 $9,000 $6,925.21 3                           0.67 $6,000 $4,049.83 $37,290.83 6 PV of Investment = Maount *Sum of PVF of 12% for year 10,11,12 =$9000*0.866124 7795.116 $

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