Fred has accepted a new job and the new company will match his contribution to a

Question

Fred has accepted a new job and the new company will match his   contribution to a retirement fund.  For   every dollar he invests, they will add a matching dollar.   If he invests $100 monthly, how   much will be in the retirement fund in 25 years if it averages a return of   5.5% APR with monthly compounding. Another retirement fund offer 6%   EAR with monthly compounding.  What   would the value of this be in 25 years for the same deposits as given above? Fred has accepted a new job and the new company will match his   contribution to a retirement fund.  For   every dollar he invests, they will add a matching dollar.   If he invests $100 monthly, how   much will be in the retirement fund in 25 years if it averages a return of   5.5% APR with monthly compounding. Another retirement fund offer 6%   EAR with monthly compounding.  What   would the value of this be in 25 years for the same deposits as given above?

Explanation / Answer

25 years = 25*12 = 300 months

Total savings monthly = 100*2 = $200

Present value of savings = 200/(1+5.5%/12) + 200/(1+5.5%/12)^2 + 200/(1+5.5%/12)^3 ....200/(1+5.5%/12)^300 =$32,568.65

Future value of savings = 32,568.65*(1+5.5%/12)^300 =$

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6% EAR with monthly compounding

Let APR rate be r

1+6% = (1+r/12)^12

APR = 5.84%

Present value of savings = 200/(1+5.84%/12) + 200/(1+5.84%/12)^2 + 200/(1+5.84%/12)^3 ....200/(1+5.84%/12)^300 =$31,514.88

Future value of savings = 31,514.88*(1+5.84%/12)^300 =$135,257.79

red has accepted a new job and the new company will match his contribution to a retirement fund. For every dollar he invests, they will add a matching dollar. If he invests $100 monthly, how much will be in the retirement fund in 25 years if it averages a return of 5.5% APR with monthly compounding. Another retirement fund offer 6% EAR with monthly compounding. What would the value of this be in 25 years for the same deposits as given above?

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