Question

Retirement planning Personal Finance Problem Hal Thomas, a 30-year-old college graduate, wishes to retire at age 60 To supplement other sources of retirement income, he can deposit $2,300 each year into a tax-deferred individual retirement arrangement (IRA) The IRA will earn a return of 15% over the next 30 years a. If Hal makes end-of-year S2,300 deposits into the IRA, how much will he have accumulated in 30 years when he turns 60? b. If Hal decides to wait until age 40 to begin making end-of-year $2,300 deposits into the IRA, how much will he have accumulated when he retires 20 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 60th 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 60th year a. If Hal makes annual end-of-year $2,300 deposits into the IRA, the amount he will have accumulated by the end of his 60th year is S(Round to the nearest cent.) b. If Hal decides to wait until age 40 to begin making annual end-of-year $2,300 deposits into the IRA, the amount he will have accumulated by the end of his 60th year is (Round to the nearest cent.) c. Using your findings in parts a and b, which of the following options better describes the impact of delaying making deposits into the IRA for 10 years (age 30 to age 40) on the amount accumulated by the end of Hal's 60th year? (Select the best answer below.) By delaying the deposits by 10 years. Hal earns a large capital gain. This gain is due to both the saved deposits of gained compounding of interest on all of the money not deposited for 10 years By delaying the deposits by 10 years. Hal is incurring a significant opportunity cost. This cost is due to both the lost deposits of $23.000 $2.300 × 10 yrs.) and the lost compounding of interest on all of the money for 10 years $23.000 ($2.300 x 10 yrs.) and the O d. If Hal makes annual beginning-of-year $2,300 deposits into the IRA, the amount he will have accumulated by the end of his 60th year is S(Round to the nearest cent.) If Hal decides to wait until age 40 to begin making annual beginning-of-year $2,300 deposits into the IRA, the amount he will have accumulated by the end of his 60th year is s(Round to the nearest cent) Both deposits change in the compounding occurs. (Select from the drop-down menus.) ▼ due to the extra year of compounding from the beginning-of-year deposits instead of the end-of-year deposits. The incremental V deposit due to the larger sum on which the last year of Vannuity is much larger than the incremental compounding on the

Answer 1

a.This is a case of ordinary annuity.

Amount accumulated in 30 years = 2,300*[{(1+0.15)³⁰-1}/0.15]

= $999,913.84

b.Amount accumulated in 20 years = 2,300*[{(1+0.15)²⁰-1}/0.15]

= $235,620.24

c.By delaying the deposits, Hal is incurring a significant opportunity cost. This cost is due to both the lost deposits of $23,000 and the lost compounding of interest on all the money for 10 years.

d.If beginning of year deposits, amount accumulated in 30 years = (1+0.15)* $999,913.84

= $1,149,900.916

Amount accumulated in 20 years = (1+0.15)* $235,620.24

= $270,963.276

Both deposits are more/higher due to extra year of compounding.

The incremental change in the 30 year annuity is much larger than on the 20 year deposit due to larger sum on which last year compounding occurs.