Question

Jamie inherited $100,000 from your grandparents, today. She has exactly 20 years to retire and she decided to put the entire amount into 20 years, 4% annual interest annuity

- assume that in addition to this initial $100,000, she also contributed $500 at the end of each month until you retire. What is the end balance, total principle, and interest? (Use equations and step by step answering)

- Finally, assume that the contributions were made at the beginning of each month. What are is the end balance, total principle, and interest now? Show step by step written work please

Answer 1

1.
Ending Balance=Future value of lumpsum+Future value of ordinary annuity=Initial amount*(1+r/12)^(12*t)+monthly payments/(r/12)*((1+r/12)^(12*t)-1)=100000*(1+4%/12)^(12*20)+500/(4%/12)*((1+4%/12)^(12*20)-1)=405645.52174161

Total Principal=Total Deposits=100000+500*12*20=220000.00

Total Interest=Ending Balance-Total Principal=405645.52174161-220000.00=185645.52174161

2.
Ending Balance=Future value of lumpsum+Future value of annuity due=Initial amount*(1+r/12)^(12*t)+monthly payments/(r/12)*((1+r/12)^(12*t)-1)*(1+r/12)=100000*(1+4%/12)^(12*20)+500/(4%/12)*((1+4%/12)^(12*20)-1)*(1+4%/12)=406256.81278509

Total Principal=Total Deposits=100000+500*12*20=220000.00

Total Interest=Ending Balance-Total Principal=406256.81278509-220000.00=186256.81278509