Question

Assume that you inherited $100,000 from your grandparents, today. You have exactly 20 years to retire and you decided to put the entire amount into 20 years, 4% annual interest annuity.

A) Assuming you did not deposit any additional amount into this account, compute your account balance by the time you retire, using the annuity calculator. Then, compute the same using a scientific calculator (not a financial one) using the appropriate formulas from the textbook and show your calculations. (Make sure the amounts are the same!)

B) 1) Now assume that in addition to this initial $100,000, you also contributed $500 at the end of each month until you retire. Compute your retirement account balance using the annuity calculator. Highlight the end balance, total principal, and total interest.

2) Now, using the relevant formulas from the textbook and a scientific calculator, reproduce the results (End Balance, Total Principal, Total Interest) showing your calculations. Highlight any issue one has to pay attention to calculating those values.

3) Finally, assume that the contributions were made at the beginning of each month. What are the above three values now? Show your computations to reproduce those values with a scientific calculator and highlight the formulas used.

C) Now, look at the first row of the “Annual Schedule” table provided by the calculator (just under the graph): Copy the values of the last three columns (Interest, End Balance, End Principal). (The values as of the end of the first year.)

Please explain how those values are computed using relevant formulas. (Do not explain assuming the use of a financial calculator.)

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