Jane Roe\'s plan is to accumulate $250,000 in her (assuming she waits N years to

Question

Jane Roe's plan is to accumulate $250,000 in her (assuming she waits N years to start saving) to have personal savings account by the time she retires at 60. $250,000 in her account when she is 60. Comment o The longer she stalls on getting started, the tougher it the pattern you observe in the table. will be to meet her objective. Jane is now 25 years old. Create a spreadsheet to complete the following table to show how much Jane will have to save each year Interest Rate per Year 8% 4% 12% N=5 N = 10 N = 15

Explanation / Answer

The total years from her present age of 25 to 60 = (60-25) = 35 years

If she has to wait for N years means her total time for saving is (35 - N).

For calculating amount of saving each year that will accumulate to $250,000, we need to use Future Value Annuity Factor for the relevant interest rate and time for savings(i.e.FVAF)

Savings each year = $250,000/FVAF(interest,years)

When Interest per year is 4%

i) N = 5 years, then time is (35-5) = 30 years

and savings each year = $250,000/FVAF(4%,30 yrs) = $250,000/58.328 = $4,286

ii) N = 10 years, then time is (35-10) = 25 years

and savings each year = $250,000/FVAF(4%,25 yrs) = $250,000/43.312 = $5,772

iii) N = 15 years, then time is (35-15) = 20 years

and savings each year = $250,000/FVAF(4%,20 yrs) = $250,000/30.969 = $8,073

iv) N = 20 years, then time is (35-20) = 15 years

and savings each year = $250,000/FVAF(4%,15 yrs) = $250,000/20.825 = $12,005

When Interest per year is 8%

i) N = 5 years, then time is (35-5) = 30 years

and savings each year = $250,000/FVAF(8%,30 yrs) = $250,000/122.346 = $2,043

ii) N = 10 years, then time is (35-10) = 25 years

and savings each year = $250,000/FVAF(8%,25 yrs) = $250,000/78.954 = $3,166

iii) N = 15 years, then time is (35-15) = 20 years

and savings each year = $250,000/FVAF(8%,20 yrs) = $250,000/49.423 = $5,058

iv) N = 20 years, then time is (35-20) = 15 years

and savings each year = $250,000/FVAF(8%,15 yrs) = $250,000/29.324 = $8,525

When Interest per year is 12%

i) N = 5 years, then time is (35-5) = 30 years

and savings each year = $250,000/FVAF(12%,30 yrs) = $250,000/270.293 = $925

ii) N = 10 years, then time is (35-10) = 25 years

and savings each year = $250,000/FVAF(12%,25 yrs) = $250,000/149.334 = $1,674

iii) N = 15 years, then time is (35-15) = 20 years

and savings each year = $250,000/FVAF(12%,20 yrs) = $250,000/80.699 = $3,098

iv) N = 20 years, then time is (35-20) = 15 years

and savings each year = $250,000/FVAF(12%,15 yrs) = $250,000/41.753 = $5,988

  

Comment : The amount of saving increased with the increase in time for waiting to save(i.e. N) and the amount of saving decreased with the increase in interest rate.

Interest rate = 4% Interest rate = 8% Interest rate = 12% N = 5 4,286 2,043 925 N = 10 5,772 3,166 1,674 N = 15 8,073 5,058 3,098 N = 20 12,005 8,525 5,988

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