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• value of each ance Annuities lab.com s onine 6-1. (Calculating the future value of an ordinary annuity Calculate the future valu edback the following streams of payments. a. £430 a year for 12 years compounded annually at 6 percent. b. €56 a year for 8 years compounded annually at 8 percent. c. $75 a year for 5 years compounded annually at 3 percent. d. £120 a year for 3 years compounded annually at 10 percent. 6-2 (Calculating the present value of an ordinary annuity) (Related to Checkpoint page 199) Calculate the present value of the following annuities. a. £350 a year for 12 years discounted back to the present at 7 percent. b. €260 a year for 5 years discounted back to the present at 8 percent. c. $3,000 a year for 8 years discounted back to the present at 6 percent. d. £60 a year for 3 years discounted back to the present at 10 percent. (Calculating the future value of an ordinary annuity) (Related to Finance for Life ing for Retirement on page 204) Mike, 30, has started a small business and wants start saving for his retirement when he turns 65. He has decided to invest £6,000 end of every year in a pension plan that earns him 6 percent compounded annually How much will Mike get when he retires? Mike then decided to keep reinvesting the profits in his business for a further five year and start saving once he is 35 years old. How much will Mike get if he starts saving the same amount and investing in the same plan as before? (Calculating the present value of an ordinary annuity) (Related to Checkpoint 6.2 on page 199) Nicki Johnson, a sophomore mechanical engineering student, received a call from an insurance agent who believes that Nicki is an older woman who is ready to re- tire from teaching. He talks to her about several annuities that she could buy that would guarantee her a fixed annual income. The annuities are as follows: Annuity Duration of the Annuity (years) Purchase Price of the Amount of Money Annuity Received per Year $50,000 $8,500 $60,000 $7,000 $70,000 $8,000 25 6-5. Nicki could earn 11 percent on her money by placing it in a savings account. Alternative she could place it in any of the above annuities. Which annuities in the table above, will earn Nicki a higher return than investing in the savings account earning 11 perco (Calculating annuity payments) (Related to Checkpoint 6.1 on page 196) James Ha rison bought a house for £180,000. He paid £20,000 upfront from his savings and to a mortgage to pay the rest for 25 years. The mortgage was to be paid in 25 equal installments that included both principal and interest. This mortgage charged o por compound interest on unpaid balance. What will his annual installments be? (Calculating annuity payments) Donna Langley bought a new luxury car forts She made a down payment of €5.000 and agreed to pay the rest over the next in eight equal annual payments that include both principal and 12 percent com interest on unpaid balance. What will these equal payments be? 25 equal ansa charged 6 percent 6-6. xury car for €50,000 next eight years at compound

Answer 1

Cal alabing futurevaues 6-1 ddimany uity F.V of an RX where i Interest Tate periods 3 R-Ained Periodic Pment here i=6. R= 430 above frmula 12 (i+61. 430 x F.V 6/ 0.06 t430 x 16.86 99 4 72 5y.07 12-56 F.VEES x O.O8 E 595-65 1 i31 RETS G3)5- 398.19 F.V 15 i101 R=f120 (-1)3-1 120x 397.20 F.VE 1 .1

Calalating value Presont 6-2 f an P.v of amnuity mount (p) x (+ Y) Y Pe amount Y IRtORCst Yate of periods o 2 heTe Y= 7.1 a n=12 Pe f 350 08M9 P.V: 350 X No k 1- +7 3గ 1- 1-07)12 PTO 3 0-07 2179.19 PEE260 Pv-260 K t- €l038-10 P-$3 000 1 1- P.V 3000 x (16 18/ 629 3

P 156 607 P. (1-1) 3 149.21 Future value Calalating wual paymen =6000 6-3 11 here mtere st Period -7 - 1 Future Value 7-686-1 6000 6.06 668 6०१ sa vin hon he 10 dears here alsomike&tost is 35ars he is till Dh Thn period To- 35 7 he te Same 9L. TM This alro CaSe amount

In &der to krow the heve Tate Pv feit of Anmvity Seen feble be mat valve =#s0, 000 Present Annua Pagmen eceived = 8580 n12yeas 1- be Pv-30, 000 35 Ptor -12, i-1) 11 5-8823 ea S8 fam present vale o SeemhatThy awnuiHy Teble Can be we Funomo m ebetween aird 141. is 13 Interest ate is7131. aald hence 1s 9 Interest Yate Savins A count is 42 hence Anmuity is best

Present value 60,000 re duratins 23ylars amount Tood Annual 7000 x P.v for (n-25, i ab ivib 9 60,000 spec ఈా = 8.511 4 7000 from the table this amounf Seen be Can we bet ween lo that ACcount 1 On Savimgi frmannuitys ghey Savings Account (nyigible TNterest Tate than Lower Present value10, o00 periodedars amounts oo Amnuet PY fada Cn-,72 21 , o00 8-15 In tere st 10, rate79 here UT onSaviw Account 11 beit option hence Savings Acount

6-5 PAnchas down pay ment f20, o0D ఈం రిరం 4 valve t1go 0 alance a uat Inffayments TCal Gulate divi ded bpelent Vale fa chr be Period 25 ya P.v fa ct and jeb 31 for Instaciments anmual 12-183Y per ga , 516.23 6-6 Purchase value:es, ovo doun pay ment - Ralance i 12/ me years P.v fector En-9, i-124.7 F4.9616 anuel Dntau ment 2€9os8.7 10 2iVA