Question

Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the "Set for Life" Prize that makes 20 consecutive annual payments of $50,000 starting immediately. There is one hitch: the eleventh payment (to be received at the end of year 10) is not $50,000 but only $20,000 (that is, this payment is $30,000 LESS than the other 20). Which of the following comes closest to the present value of the prize if interest rates are 6%? a. $ 551,529 b. $ 591,154 c. $ 743,867 d. $ 686,430 o e. $ 635,849

Answer 1

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05 02 х a qx ENG 36 22 03 01 2020 AC450 AB AD AE AF AJ AC AG АН Al AK 427 428 429 PRESENT VALUE OF ALL LOTTERY PAYMENTS = 430 50000.00 [RECEIVED IMMEDIATELY] 50000 + 431 STEP 1 432 50000 X PVIFA @ 6%, FOR 9 YEARS + 340084.61 [=50000*(1/0.06)*(1-(1/(1+0.06)^9))] 11167.90 (=20000/(1+0.06)^10] STEP 2 433 STEP 3 20000 X PVIF @6% FOR 10 YEARS + 434 50000 X PVIFA @ 6%, FOR 9 YEARS X PVIF @6%, 10 YEARS STEP 1+ STEP 2 + STEP 3 + STEP 4 189901.47 [=50000* (1/0.06)* (1-(1/(1+0.06)^9)) X (1/(1+0.06)^10)] STEP 4 435 ANSWER = 591153.98 436 ANSWER : b 591154 437 438 WE HAVE DIVIDED WHOLE SUM IN 4 PARTS NOTE 439 440 FIRST, 50000 RECEIVED IMMEDIATELY 441 SECOND, 50000 RECEIVED FROM YEAR 1 TO YEAR 9 442 THIRD, 20000 RECEIVED AT THE END OF 1OTH YEAR 443 FOURTH, 50000 RECEIVED FOR LAST 9 YEARS WE HAVE TO DISCOUNT ABOVE PV OF 50000 FOR 10 YEARS TO GET VALUE AS OF TODAY 444 445 446 447 448 449 450 451 452 453 454 455 , . | PM, PMT | l DILUTION | DOLLAR COST AVG | EXPO ear FVA LOAN OPTIONS pv, lv, annuily CAP STRU VALUE 53 ST. . O : O | LOCK BOX loan wilth points NPER APR CPI s2 pva