Assume an 8% interest rate and annual compounding in the following two scenarios

Question

Assume an 8% interest rate and annual compounding in the following two scenarios: (1) Assume Ace will not retire for 5 years. Beginning with the end of year 6, he will make the first of ten annual withdrawals of $100,000 from his retirement account (i.e., through year 15). What must Ace have in his retirement account today in order to make those annual withdrawals? (2) What must Ace have in his retirement account today if he makes the first of the ten annual withdrawals at the beginning of year 6 (assuming everything else is the same as scenario (1) above)?

Explanation / Answer

What must Ace have in his retirement account today in order to make those annual withdrawals? If withdrawel is make in the ending of every year If ace with draw every year ending then he will get interest for opening balance other wise if he withdraw on beginning of every year then he will not get interest on withdrawel amount. Year Opening Blance With draw Amount Interest earned @ 8% Closing Balance 1                  457,000                                    -                                  36,560                 493,560 2                  493,560                                    -                                  39,485                 533,045 3                  533,045                                    -                                  42,644                 575,688 4                  575,688                                    -                                  46,055                 621,743 5                  621,743                                    -                                  49,739                 671,483 6                  671,483                         100,000                                53,719                 625,202 7                  625,202                         100,000                                50,016                 575,218 8                  575,218                         100,000                                46,017                 521,235 9                  521,235                         100,000                                41,699                 462,934 10                  462,934                         100,000                                37,035                 399,969 11                  399,969                         100,000                                31,997                 331,966 12                  331,966                         100,000                                26,557                 258,523 13                  258,523                         100,000                                20,682                 179,205 14                  179,205                         100,000                                14,336                    93,542 15                    93,542                         100,000                                   7,483                      1,025 Total                     1,000,000 What must Ace have in his retirement account today in order to make those annual withdrawals? If withdrawel is make in the begining of every year from 6th year Year Opening Blance With draw Amount Interest earned @ 8% Closing Balance 1                  500,000                                    -                                  40,000                 540,000 2                  540,000                                    -                                  43,200                 583,200 3                  583,200                                    -                                  46,656                 629,856 4                  629,856                                    -                                  50,388                 680,244 5                  680,244                                    -                                  54,420                 734,664 6                  734,664                         100,000                                50,773                 685,437 7                  685,437                         100,000                                46,835                 632,272 8                  632,272                         100,000                                42,582                 574,854 9                  574,854                         100,000                                37,988                 512,842 10                  512,842                         100,000                                33,027                 445,870 11                  445,870                         100,000                                27,670                 373,539 12                  373,539                         100,000                                21,883                 295,422 13                  295,422                         100,000                                15,634                 211,056 14                  211,056                         100,000                                   8,884                 119,941 15                  119,941                         100,000                                   1,595                    21,536 Total                     1,000,000

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