Question

Decision #2:  Planning for Retirement

 

Evan and Gina are 22, newly married, and ready to embark on the journey of life.   They both plan to retire 45 years from today.  Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $2700 per year to prepare for retirement.   Gina just told Evan, though, that she had heard that they would actually have more money the day they retire if they put $2700 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).   Please help Evan and Gina make an informed decision:   

 

Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.2% annually.  

 

(Please do NOT ROUND when entering “Rates” for any of the questions below)

        b)     How much money will Evan and Gina have in 10 years if they put $2700 per year away for the next 10 years?

 

b2)  How much will the amount you just computed grow to if it remains invested for the remaining

 35 years, but without any additional yearly deposits being made?

Answer 1

REF::  https://www.homeworklib.com/question/1543983/decision-2-planning-for-retirement-evan-and-gina  

Answer 2

A. Investing $2,700 per year for next 35 years

Future value = C x [(1+r)ⁿ-1/r],

C = Annual cash flow at the end of each period; $ 2,700 in the instant case

R = Rate of interest; 7.2% in the instant case

n = Number of payment; 35 in the instant case.

Applying the above formula in the instant case,

Future value shall be

= 2,700 [11.39771-1/0.072)

= $ 3,89,914

B. Investing $2,700 per year for next 10 years

Future value = C x [(1+r)ⁿ-1/r],

C = Annual cash flow at the end of each period; $ 2,700 in the instant case

R = Rate of interest; 7.2% in the instant case

n = Number of payment; 10 in the instant case.

Applying the above formula in the instant case,

Future value shall be

= 2,700 [2.004231-1/0.072)

= $ 37,658.68

C. Future Value of above amount at the end of next 35 years

Future Value = P(1+r)^t

P = Principal value; $ 37,658.68 in the instant case

R = Rate of interest; 7.2% in the instant case

t = time period; 35 in the instant case

Future value shall be

= 37,658.68 (1+0.072)³⁵

= $ 429,222.60

D. Investing $2,700 per year for next 45 years

Future value = C x [(1+r)ⁿ-1/r],

C = Annual cash flow at the end of each period; $ 2,700 in the instant case

R = Rate of interest; 7.2% in the instant case

n = Number of payment; 45 in the instant case.

Applying the above formula in the instant case,

Future value shall be

= 2,700 [2.004231-1/0.072)

= $ 819,136.60

It may be seen that this is actually the aggregate of the amount computed in Para A and Para C above.

E. Investing $225 every month for next 45 years

Future value = C x [(1+r)ⁿ-1/r],

C = Monthly cash flow at the end of each month; $ 225 in the instant case

R = Rate of interest for each month; 0.6% (7.2/12) in the instant case

n = Number of payment; 540 (45*12) in the instant case.

Applying the above formula in the instant case,

Future value shall be

= 225 [25.287715-1/0.006)

= $ 910,789.31

F. $1,000,000 after 20 years

Future value = C x [(1+r)ⁿ-1/r],

Future value is given as $ 1,000,000

C = Annual cash flow at the end of each period to be computed

R = Rate of interest; 7.2% in the instant case

n = Number of payment; 20 in the instant case.

Applying the above formula in the instant case,

1,000,000 = C x [4.01694-1/0.072)

C = $ 23,865.21