Question

Today is Derek's 25th birthday. Derek has been advised that he needs to have $2,081,021.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 9.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 29.00th birthday and ending on his 65th birthday. How much must those deposits be?

Answer 1

Question ! Timeline 37 deposits to be made 64 65 1 Year 25 29 30 Depents nii+.com) *(1+.one i nlit.or)' *(1+.00) Interest Rate = 9.1. let deposit be a The resultart equation shall be ) n (1+.09) + x (17.09) + --- -- + (1+.09)' + x[17.09) = 2,081,021 Taking a common from the equation we shall get u cit.oqja + (1+.00+--1.00° ] = 2,081,021 nx future value Annuity factor (9.1 37 years) = 2,081,021 nx 258.376 = 2,081,021 W = $ 8054.23 8054. 23 The arrual deposit that Derek should make is $ 8054.23 to achieve his desired anourt of $2,081,021.

9th starting from 2 otal - Calculation of future value Annuity factor Please note that the deposits are made stara Birthday to 65th birthday this there are in to 3.7 deposits being made the cash flows are occuring at end of the year herce it is question of orderary annuity. Future value Annuity factor = (1+r) -1 - r = (1 + 0.09) - 0.09 24.25 384 - 1 - 0,09 = 258.376

Question 2 G Question 2 Timeline - 6 years Year o Today Year 6 $3644 29 61 r) 6 Rate of Interest = r . Time I years = t future Value = Presest value (ltr) 3644 = 2960 (ltr) (1+r) = 1 3644 96 2961 er? (1.23066) , = 1.035 20 -1 calculation is shown bele} = 0.035 20 ie 3.520.7. Thus, account earned 3.520.1. per year. Calculation Please note for solving A equation, the process is as follows: Step 1 : Press A, then in 12 times Step 2 : Press o a Step 3 : Press LABI Step 4 : Press ] ] Step 5 : Press 1x = 12 times

wwwwwwwwwwwwwwwwww For our question : Step 1 : Press 11.23066 ir 12 times Result will be 1.00005067 Step a : Press E 1 Result = 0.00005067 Step 3: Press x1 YG Result = 0.00000 8447 Step 4: Press I [1] Result = 1.00000 8447 Step 5 : Press 1x = 12 times Result = 1.035204