Question

This assignment highlights the importance of using the "effective annual rate" and how to obtain a periodic rate that will provide us with the desired effective annual rate.

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.)

Answer 1

ANSWER:

Requirement A:

Principal (P)= $100,000

Annual Interest Annuity (r) = 4%

Time (t) = 20 years

Calculating the account balance after 20 years, using Annuity Calculator:

Principal	$100,000
Interest	$119,112.31
Ending Balance	$219,112.31

Calculating the account balance after 20 years, using textbook formulas:

FV = A [(1 + r)t - 1] / r

= 100,000 [(1 + 4%)20 - 1] / 4%

= 100,000 [(1.04)20 - 1] / 0.04

= 100,000 (29.75) = $2,975,000

Requirement B:

Starting Principal = $100,000

$500 deposited at the end of each month until retirement

The account balance after 20 years, using Annuity Calculator:

Principal	$220,000
Interest	$181,033.18
Ending Balance	$401,033.18

Starting Principal = $100,000

$500 deposited at the end of each month until retirement

So, total amount deposited in 20 years = $500 * 12 * 20 = $120,000

Therefore, Principal = 100,000 + 120,000 = $220,000

Calculating the account balance after 20 years, using textbook formulas:

FV = A [(1 + r)t - 1] / r

= 220,000 [(1 + 4%)20 - 1] / 4%

= 220,000 [(1.04)20 - 1] / 0.04

= 220,000 (29.75) = $6,545,000‬