Hello kindly answer the 1-5 only with solution. I already post the guide references below.. Thank you so much!

2.7 EQUATIONS OF VALUES As discussed in Chapter 1, the value of money at any given time depends upon the time elapsed since the money was paid in the past or upon the time which will elapse in the future before it is paid. Two sets of Obligations can be compared by equation of values. One of the properties of compound interest is that the choice of the comparison time makes no difference in the answer obtained. Thus. there are different equations of value for each comparison time but they all produce the same answers. However, under the simple interest or simple discount. the choice of comparison time affects the answers obtained. The techniques in solving equation of value problems discussed in 1.6 are similar in this section. If the comparison time is located at the middle part of the time diagram, all obligations at the left are brought to the comparison time by the process of accumulation and all obligations at the right are brought back to the comparison time by the process of discounting. If any obligations bear interest, we rst compute the mamrity values before bringing them to the comparison time. If the comparison time is located at the due date of the last Obligation. all obligations along the lime diagram are brought to the comparison time by the process of accumulation. If the comparison time is located at the due date of the rst obligation, all obligations along the time diagram are brought back to the comparison time by the process of discounting. 56 COMPOUND [NTEREST 2.7 Equations of Values Example 24. Leigh has the following debts: 1,000 to be paid at the end of the seventh year; 800 at the end of the fourth year and 500 at the end of 2 1/2 years. If the settlement rate is 10% compounded semiarmually, what single amount to be paid now will equitably replace the set of obligations? OLD OBLIGATIONS NEW OBLIGATIONS --_ - E_- Solutions: A. Comparison time: year 0, settlement rate = 10%, m = 2 1. Bring all obligations to the comparison time. Since all old obligations are at the left of the comparison time, they will be brought to year 0 by discounting. Time diagram for this solution is shown on the next page. TIME DIAGRAM Payment x Comparison time W 0 1 2 3 4 5 6 7 8 ' t= 2.5 yrs 500 800 1,000 t: yrs 4 2. Form the equation by separating the old obligations from the new obligation, and solve the resulting equation. x = 500(1.05)'5 + 1300(105)'s + 10000.05)-I4 x = 1,438.30 E 500.]: 1.05 A - 5 + 800 x 1.05 " - 8 +1000x 1.05 A - 14 : 1,438.30 R. Comparison time: year 4, settlement rate : l0%, m : 2 1. Bring all obligations to the comparison time. Since the comparison time is at the middle, all obligations at the left are accumulated to the comparison time while all obligations at the right are discounted to the comparison time. TIME DIAGRAM Payment x Comparison time W 0 l 2 3 4 5 6 7 8 500 8% 1.000 t: 1.5 yrs 2. Form the equation by separating the old obligations from the new obligation, and solve the resulting equation. 57 COMPOUND INTEREST 2.7 Equations of Values 1; (1.05)B = 500(105)'3 + 800 + 1000(1.05)*5 x = 1,438.30 C. Comparison time: year 7, settlement rate = 10%, m = 2 1. Bring all obligations to the comparison time. Since all old obligations are at the right of the comparison time, they will be brought to year '1' by accumulating. TIME DIAGRAM Payment x Comparison time W 0 1 2 3 4 5 6 7 8 500 800 1:000 2. Form the equation by separating the old obligations from the new obligation, and solve the resulting equation. x(1.05)14 = 50011.05)9 + 8000.05)6 + 1000 x : 1,433.30 The results show that the choice of the comparison date will not affect the value. It is easier to use the comparison year where the unknown is placed. Example 25. Jack owes the following obligations: 3.000 due at the end of 2 years, 4,000 due at the end of 3 years with 7 V2% simple interest, 1,500 due at the end of 6 years at 4% cenverted semiannually and 2,800 due at the end of 3 years at 3% compounded quarterly. At 5% (settlement rate) compounded quarterly, what single payment at the end of 4 years will equitably replace the obligations? Computations of maturity values are shown below. OLD OBLIGATIONS NEW OBLIGATION 3000, due aerz s 4000, 7.5% Sim-1e interest, due after3 4000 1+0.075 3 =4,900 12 1,500,491, m = 2, due after 6 yrs 1500[1+ LS4] =1,902_35 _ 0.03 32 2.800. 3% m = 4, due after 8 yrs 2800['I + T] = 355631 Solutions: A. Comparison time: year 5, settlement rate = 5%. m = 4 1. Compute the maturity value of the obligations which is already done on the table above. 2. Bring all obligations to the comparison time. Obligations at the left are accumulated to year 5 and obligations at the right are discounted to year 5. 53 COMPOUND INTEREST 2.7 Equations of Values TIME DIAGRAM Payment 3: Comparison time W 0 l 2 3 4 5 6 7 8 3.000 4.000 1,500 2,300 MV 4,933 1,902.36 3.55 6.31 ' ' t=1 t=2yrs t: yrs 13:1);1'5 3. Form the equation by separating the old obligations from the new obligation, and solve the resulting equation. x(1,0125)4 = 300000125)\" + 400011 0125)8 +190235(10125)'4 + 3555310 0125112 X _ 3000(10125)12 + 4000(1,0125)8+100235(10125) 4 + 3555310 0125)42 (1.0125)4 x = 13,100.76 (30001: 1.0125 A 12 + 4900:: 1.0125 A s + 1902.363: 1.0125 A - 4 + 3550.31 1: 1.0125 A - 12 ) +1.0125 A 4 = 13,100.76 B. Comparison time: year 8 After the Computation of the maturity values of the obligations, place all values along the time diagram, accumulate them to the comparison time, and form the equation. TIME DIAGRAM Payment 3; Comparison time :' W 0 1 2 3 4 5 6 7 8 3,000 4,000 1,500 2,800 MV 4,900 1,902.36 3'55631 - t = 6 yrs T. x(1,0125)15 = 3000110125)24 + 490101 .0125)\" +190235(10125)3 + 35553111012533:2 X = 3000(10125)24 + 4900(1.0125}20+1002 30(10125)8 + 3555.31(1 .0125)32 (1.0125)16 x : 13,100.76 C. Comparison time: year 2 Discount all values to the comparison time, form the equation of values and solve the resulting equation. 59 COMPOUND INTEREST 2.7 Equations of Values TIME DIAGRAM Comparison little Paymerrt x W 0 1 2 3 4 5 6 7 8 3,330 4,000 1,500 2,800 _ MV 4.900 1.90236 3,556.31 ' t = 1 yr 4t24yrs *y 1(10125)8 =3000+ 4900(10125)'4 +100235(10125)'16 + 35553100125)'24 x _ 3000 + 4900110125!" 4+1902.35!1 0125115 + 35503111 01251" 24 (10125)" 8 x : 13,100.76 Example 26. With the same set of obligations in example 24, find the two equal payments at years 3 and 4 that will equitably replace the debts. Solution: Comparison time may either be year 3 or 4 since the unknowns are on those years. In this solution the comparison time is year 4. The resulting equation of values is 500(1.05) + 800 + 1000(1.05) 6 = x(1.05)-2 +x 1.907029478x = 1.45343404 X = 762.15 Thus, to replace the obligations, 762.15 must be paid on the third and fourth years. Example 27. With the same sets of obligations and interest rates in example 25, find the two equal payments on year 5 and 7 that will equitably replace the debts. Solution: Use year 5 as the Comparison date. The resulting equation of values is 3000 (1.0125 )12 + 4900 (1.0125 )8 + 1902.36 (1.0125 ) 4 + 3556.31 (1.0125 ) 12 =x(1.0125 ) 8 +x 3000(1.0125) 2 + 4900(1.0125)8 + 1902.36(1.0125)-4 + 3556.31(1.0125) 12 =0.9054x +x 1 9054x = 3000(1 0125) 2 + 4900(1 0125)8 +1907 36(1 0175) 4 + 3556 31(1 0175)12 X = = 3000(1.0125) 2 + 4900(1.0125)8 + 1902.36(1.0125) 4 + 3556.31(1.0125)-12 1.9054 X =7,225.88 Thus, to replace the obligations, 7,225.88 must be paid on the fifth year and seventh year.EXERCISES 2.7 01. 03. 05. 10. An obligation worth 45,000 is to be paid by installment basis. The following are the installments: 10,000 due at the end of 2 years, 5,000 due at the end of 5 years, and a nal payment at the end of 7 years. Find the nal payment if money is worth 7.5% with comparison time at the end of A) 2 years; B) 5 years; C) 7 years. Mr. Lopez buys a property worth 145,000 cash. He pays 40,000 as down payment; 25,000 at the end of 2 years, 10,000 at the end of 5 years, and a nal payment at the end of 9 years. Find the nal payment if money is worth 7.5% with comparison time at the end of A) 2 years; B) 5 years; C) 9 years. To accumulate 100,000 at the end of 10 years. a person agrees to pay 30.000 at once. 10,000 at the end of 3 years, and to make further payment at the end of 6 years. Find the payment at the end of 6 years if the nominal rate of interest is 6% converted quarterly. In return for a promise to receive 60,000 at the end of 8 years, a person agrees to pay 10,000 at once, 20,000 at the end of 3 years, and to make further payment at the end of 5 years. Find the payment at the end of 5 years if the nominal rate of interest is 8% converted semiannually. What single payment to be paid now will settle the following obligations if the settlement rate is 8% compounded semiannually; 1,250 due in 1 1/2 years at 8% simple interest rate; 3,250 due in 3 years at 7% compounded semiannually and 5,000 due in 7 years at 6% compounded quarterly? What single payment to be made immediately will settle the following obligations if money is worth 6% compounded quarterly; 2,500 due in 2 years at 7% compounded quarterly; 3,000 due in 3 years at 6.5% compounded quarterly and 4,000 due in 6 years at 4% compounded semiannually? Jeremy borrowed 6,000 om lay on Sept 15, Y and 7,000 on Sept 15, Y+1. He paid 2,000 on Sept 15, Y+2, 3,000 on Sept 15, Y+3 and 5,000 on Sept 15, Y+5. What nal payment is needed on Sept 15, Y+7 if money is worth 6.5 % to discharge the remaining liability? Christian borrowed 2,000 from Mark on June 1, Y and 5,000 on June 1, Y+2 agreeing that money is worth 5% compounded annually. Christian paid 1,500 on June 1, Y+3, 1,400 on June 1, Y+4 and 2,700 on June 1, Y+5. What additional sum should Christian pay on June 1, Y+8 to discharge all remaining liability? Eric owes Bert the following obligations: 10,000 due at the end of 10 years; 20,000 due at the end of 5 years with interest at {0.05, m =2} and 30,000 due at the end of 4 years with interest from today at 4%. Eric is allowed to discharge his obligations by two equal payments: at the end of the third year and sixth year. If Bert admits that money is worth 6% compounded semiannually, find Eric's equal payments. Mr. Santos owes Mr. Reyes the following obligations: 5,000 due at the end of 5 years; 2,500 due at the end of 3V2 years with accumulated interest from today at {0.04,m =4} and 1,250 due at the end of 1 year with accumulated interest from today at {0.06, In = 2}. Mr. Santos is allowed to discharge his obligations by two equal payments: at the end of the second year and fourth year. If Mr. Reyes agrees that money is worth 5% compounded annually, nd Mr. Reyes's equal payments