Question

  Hal​ Thomas, a 30​-year-old college​ graduate, wishes to retire at age 65. To supplement other sources of retirement​ income, he can deposit ​$2 comma 000 each year into a​ tax-deferred individual retirement arrangement​ (IRA). The IRA will earn a return of 13​% over the next 35 years.

a.  If Hal makes​ end-of-year ​$2 comma 000 deposits into the​ IRA, how much will he have accumulated in 35 years when he turns  65​?

b.  If Hal decides to wait until age 40 to begin making​ end-of-year ​$2 comma 000 deposits into the​ IRA, how much will he have accumulated when he retires 25 years​ later?

c.  Using your findings in parts a and ​b, discuss the impact of delaying deposits into the IRA for 10 years​ (age 30 to age 40​) on the amount accumulated by the end of​ Hal's 65 th year.

d.  Rework parts ​a, b, and c assuming that Hal makes all deposits at the​ beginning, rather than the​ end, of each year. Discuss the effect of​ beginning-of-year deposits on the future value accumulated by the end of​ Hal's 65 th year.

Answer 1

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Q v 1 = 06-22 ENG 27-01-20206 CV944 2 CQ X CR fic CS CT CU CV CW C X CY CZ DA 944 945 946 947 948 949 950 951 952 953 954 955 956 FUTURE VALUE OF ANNUITY PMT YEARS RATE FUTURE VALUE [ACCUMULATED AMOUNT] 2000 35 13.00% 1093361.64 (=FV(CW951, CW950,-CW949)] 2000 957 958 IF YOU WAIT FOR 10 YEARS THEN YOU WILL MAKE 25 PAYMENTS PMT YEARS RATE FUTURE VALUE 25 960 13.00% 311239.11 (=FV(CW959,CW958,-CW957)] 961 962 IF DEPOSIT IS MADE FOR FIRST 10 YEARS ALSO THAT IS TOTAL 35 YEARS EXTRA AMOUNT DEPOSITED = 20000 INCREASE IN ACCUMULATED AMOUNT = 782122.53 963 964 965 966 967 IN OTHER WORDS, IF ALL 35 YEARS DESPOSIT IS MADE YOU RECEIVE MORE THAN 3 TIMES AMOUNT THAN INVESTED FOR 25 YEARS [1093361.64/311239.11 = 3.51) 968 969 970 ... pv, fv, annuity CAP STRU VALUE PM, PMT loan with points LOCK BOX DILUTION DOLLAR COST AVG EXPO NPER APR CPI ear FVA pva s2 ... I

v ( 1 06-22 ENG 27-01-20206 . fix X CR CS CT CU CV CW | CX CY CZ DA - 2000 CV990 | CR 969 970 971 972 973 974 975 976 977 978 979 980 35 FUTURE VALUE OF ANNUITY DUE PMT YEARS RATE FUTURE VALUE [ACCUMULATED AMOUNT] 13.00% 1235498.65 (=FV(CW974, CW973,-CW972,,1)] 981 IF YOU WAIT FOR 10 YEARS THEN YOU WILL MAKE 25 PAYMENTS PMT YEARS RATE FUTURE VALUE 982 2000 25 13.00% 351700.20 [=FV(CW982,CW981,-CW980,,1)] 983 The amount is still higher because you will get one year more interest as you deposited in beginning of the year 984 985 986 987 988 989 990 991 992 993 994 995 ... pv, fv, annuity CAP STRU VALUE PM, PMT loan with points LOCK BOX DILUTION DOLLAR COST AVG EXPO NPER APR CPI ear FVA pva s2 ... 7

Answer 2

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