Question

1 Due Date: October 31, 2019 PGE 411 Homewok-3 3. It is desired to make an initial lump sum investment that will provide for a withdrawal of $500 at the end of year 1, $600 at the end of year 2, and amounts increasing $100 per year to a final $2400 at the end of year 20. How great an initial investment will be required if it earns 12% compounded annually? 4. It is desired to invest a lump sum of money on a boy’s 4th birthday to provide him $2,000 on each birthday from the 18th to the 22nd, both inclusive. If the interest of 12% can be obtained from the investment, what lump sum must be invested? 5. Assume that in the circumstances described in Problem 4, it is not practicable to invest the entire lump sum indicated by your calculations. $500 will be invested on the 4th birthday and a uniform annual deposit in the fund will be made on the 5th and 12th birthdays, both inclusive. Assuming 12% interest, what must be the annual deposit from the 5th to 12th birthdays? 6. Solve the following, using interest at 12% compounded annually: (a) What is the amount that will be accumulated in a fund at the end of 15 years if $200 is deposited in the fund at the beginning of each of the 15 years? (b) Uniform deposits are to be made on January 1 of 2012, 2013, 2014 and 2015 into a fund that is intended to provide $1,000 on January 1 of 2025, 2026, and 2027. What must be the size of these deposits? 2

Answer 1

2400 So 2 3 - - 20 (i=1200%. I V x=p= ? Here A = 500 G= 1oo i = 12:00) Present P= value of gradient Series 100 1P, 127, 20) + 500 (PA, 12%., 20) = 100 ( 44.9676) + 500(7.4694) p= $ 8231.45 A= $2000 18 19 20 21 22 5 years A 2,000 - 13 14 15 16 17 5 years

Рас арове (*) , 12., 5 ) 2 обох 3. bo4 8 = = $22o9. 4 : P= {ээ 9 ( vr, 1ъ». , 13) - 2 2 o3. Схо- 22917 ГР Т 1 (52-224) 52. 2 2 4 Az 2000 а --- А — 13 14 15 11 12 18 S 89a 8 [t=12». Soo H-?) 8 неят о» MeV = - 5oo — А ( Р/А, 12 /. , 8) + $ 3052- 224 Ах (4 - 9691) = 1152 224 :. А = $231 - 95 А и 23

i= 12%. A = 200 F: A (FIA, i, n) = 200 (FIA, 12%.,15) = 200x (32:28) F = $ 74.567 Ill 14 15 16 17 3 years O: NPV = -A (P/A, 12%., 4) + 1000(!/ A, 123, 3)* (P/F, 121, 14) ... A x( 3.0373) = 1000x12.4018)*(0.20462) - A = $ 1618) AY $ 1621