Question

BUSI 320 Problem#3 (Decision #2)

Decision #2: Planning for Retirement

Mike and Joy are 25, 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 $2400 per year to prepare for retirement. Joy just told Mike, though, that she had heard that they would actually have more money the day they retire if they put $2400 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - than they would have 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 Mike and Joy make an informed decision:   

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

1. How much money will Mike and Joy have in 45 years if they do nothing for the next 10 years, then puts $2400 per year away for the remaining 35 years?

2. How much money will Mike and Joy have in 10 years if they put $2400 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?

3. How much money will Mike and Joy have in 45 years if they put $2400 per year away for each of the next 45 years?

4. How much money will Mike and Joy have in 45 years if they put away $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust the 7.2% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal)   Example of rounding: .062134 = .06213 or 6.213%

5. If Mike and Joy wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years in order to have $800,000 saved up on the first day of their retirement 45 years from today?

Answer 1

Amount Invested per year = P = $2400

Rate of Interest = r = 7.2%

(a) Investment made from Year 11 to Year 45 = $2400

=> Value in Account = P(1+r)³⁴ + .... + P(1+r)² + P(1+r) + P = P[(1+r)³⁵ -1]/r = 2400[(1+0.072)³⁵ -1]/0.072 = $346590.23

(b) Amount Saved for first 10 years = $2400

Value of savings after 10 years = P(1+r)⁹ + .... + P(1+r)² + P(1+r) + P = P[(1+r)¹⁰ -1]/r = 2400[(1+0.072)¹⁰ -1]/0.072 = $33474.37

(b-2) Value of this amount at Year 45 = 33474.38*(1+r)³⁵ = $381531.17

(c) Amount invested each year for 45 years = $2700

Value in account after 45 years = P(1+r)⁴⁴ + .... + P(1+r)² + P(1+r) + P = P[(1+r)⁴⁵ -1]/r = 2400[(1+0.072)⁴⁵ -1]/0.072 = $728121.39

(d) Amount invested each month P = $200

Number of months = 45*12 = 540

Interest Rate = r = 0.072/12

Value after 45 years = P(1+r)⁵³⁹ + .... + P(1+r)² + P(1+r) + P = P[(1+r)⁵⁴⁰ -1]/r = 200[(1+0.072/12)⁵⁴⁰ -1]/(0.072/12) = $809590.50

(f) Let the amount saved each year for 20 years be X

Value in 25 years = $800000

=> 800000 = P(1+r)¹⁹ + .... + P(1+r)² + P(1+r) + P = P[(1+r)²⁰ -1]/r = X[(1+0.072)²⁰ -1]/0.072

=> X = 800000/[[(1+0.072)²⁵ -1]/0.072] = 800000/41.90 = $19092.17