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

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PLEASE SHOW WORK

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