Using the time value of money to compute the present and future values

QUESTION

Using the time value of money to compute the present and future values of single lump sums and annuities You plan to save using one of the following two strategies: (1) save $3,000 a year in an IRA beginning when you are 22 and ending when you are 52 (30 years), or (2) wait until you are 37 to start saving and then save $6,000 per year for the next 15 years. Assume you will earn the historic stock market average of 14% per year.
Requirements
1. How much out-of-pocket cash will you invest under the two options?
2. How much savings will you have accumulated at age 52 under the two options?
3. Explain the results.
4. If you were to let the savings continue to grow for 10 more years (with no further outof- pocket investments), what would the investments be worth when you are age 62?
Solution: 1) Under option 1, when i invest $3,000/year at 22 years and end at 52 years, n=30 years Rate of return=14% Present value of annuity= Annuity [(1+rate of return)^n “ 1] / (rate of return* (1+rate of return) ^ n) = 3000*[(1+14%)^30 “ 1] / (14% * (1+14%) ^ 30) =$21016.90 œout of pocket expenses Under option 2, when I invest $6,000 for n=15 years, rate of return=14% Present value of annuity= Annuity [(1+rate of return)^n “ 1] / (rate of return* (1+rate of return) ^ n) =6,000*[(1+14%) ^ 15 -1] / (14% * (1+14%)^15) =$36,840 œout of pocket expenses 2. Under option 1, when I invest $3,000/year at 22 years and end at 52 years, n=30 years Rate of return=14% Future value of annuity=Annuity [(1+rate of return)^n “ 1] / (rate of return) =3000*[(1+14%)^30 “ 1] / 14% =$1,070,360.54 œsavings at age 52 Under option 2, when I invest $6,000 for n=15 years, rate of return=14% Future value of annuity= Annuity [(1+rate of return)^n “ 1] / (rate of return) =6000*[(1+14%)^15- 1] / 14% =$263,054.48 œsavings at age 52 3. Under option 1 when the savings are 3000you can and time is 30 years the present value of annuity is low at $21017 approx Under option 2 when the¦

savings are doubled to 6000 you can and time is halved to 30 years the present value of annuity is high at $36840 approx Under option 1 when the savings are 3000you can and time is 30 years the futurevalue of annuity is high at $ 1,070,360.54 approx Under option 2, when I invest $6,000 for n=15 years, rate of return=14% the future value of annuity is low at $263,054 If the cash reserve is low and you invest for a longer time the present value of annuity is low while the future value of annuity is high. If the cash reserve is high and you invest for a shorter period of time the present value of annuity is low and future value of annuity is high. 4. Under option1 the future value at 62 =$1,070,360.54*(1.14^10) =$3,968,063.41 Under option 2 the future value at 62 =$263,054.48 *(1.14^10) =$975,201.18

ANSWER:

CLICK REQUEST FOR  AN EXPERT SOLUTION