Question

Gabriela inherits money from her aunt. She gets $100,000 from her aunt, today. She have exactly 20 years to retire and she decided to put the entire amount into 20 years, 4% annual interest annuity.”

A. The answer to this problem is $219,112.31. A total principle of $100,000.00 and total interest of $119,112.31.

Show work with finance formulas like annuity step by step for this problem to get this answer.

b.Next assume that in addition to this initial $100,000, she also contributed $500 at the end of each month until she retires.

Answers: End balance: $401,033.18

Total principle: $220,000.00

Total interest: $181,033.18

Show the work with necessary finance formulas to get this answer.

C. Finally, assume that the contributions were made at the beginning of each month. What are the above three values now?

Answers: End Balance - $401,628.74

Principle - $220,000

Interest - $401,628.74 - $220,000 = $181,628.74

Show your computations to reproduce those values with hand written formulas and highlight the formulas used.

Answer 1

1.
End value=Present value*(1+rate)^t
=100000*1.04^20
=219112.31430334

Principal=100000

Interest=End value-Principal=219112.31430334-100000=119112.31430334

2.
rate compounded monthly=(1+4%)^(1/12)-1=0.327373978%

Future value of ordinary annuity=periodic amount/periodic rate*((1+periodic rate)^n-1)=500/0.327373978%*((1+0.327373978%)^(12*20)-1)=181920.86450452

End Balance=End balance from lumpsum+End balance from annuity=181920.86450452+219112.31
=401033.18

Total principal=Lumpsum+Total annuity deposits=Lumpsum+Periodic annuity*n=100000+500*12*20=220000.00

Interest=End Balance-Total principal=401033.18-220000.00=181033.18

3.
Future value of annuity due=periodic amount/periodic rate*((1+periodic rate)^n-1)*(1+periodic rate)=500/0.327373978%*((1+0.327373978%)^(12*20)-1)*(1+0.327373978%)=182516.42607546

End Balance=End balance from lumpsum+End balance from annuity=182516.42607546+219112.31
=401628.73607546

Total principal=Lumpsum+Total annuity deposits=Lumpsum+Periodic annuity*n=100000+500*12*20=220000.00

Interest=End Balance-Total principal=401628.73607546-220000.00=181628.73607546