Question 1 -

Irene deposited a total of $400,000 for a period of 5 years in two saving accounts; the first carries a 5% annual interest rate and the second carries a 7% annual interest rate. The interest in each account is credited to the accounts at the end of each year. At the end of the five year period Irene received a total sum of $529,452 from both accounts.

How much did Irene deposit in each of the accounts?

Question 2 -

On January 1, 2007, Bob made a deposit in a savings account. Two years later the balance in the account was $36,000, and four years later the balance was $51,840.  Assume Bob did not withdraw any funds from the account.

a) What is the account's annual interest rate?

b) What was the account's principal on January 1, 2007?

Question 3 -

On January 1, 2008 you were given the following post-dated checks:

Assume that the monthly interest rate is 2%.

a) Calculate the present value of each check.

b) Suppose you got only one check with a date of 30 June 2008.  If this check has the same present value as the four checks above, what is its amount?

Question 4 -

The following table gives the expected cash flow from three of your assets:

The payments on each asset are made at the end of the year, and the annual interest rate is 10%.

Which of your assets is the most valuable?

Question 5 -

You are presented with two options:

Option A - An annual payment of $1,000 for three years at the end of each year, and $1,200 for an additional ten years starting at the end of the fourth year.

Option B - A one-time lump-sum payment of $15,000 at the end of the fifth year.

Assume an annual interest rate of 5%.

Which option would you prefer?

Question 6 -

To pay off a debt of $165,000, Mrs. Smith has to pay an amount of $X for 7 years and an amount of $2X for an additional 15 years. The payments are made at the end of each year with an annual interest rate of 9%.  What is the value of X?

Question 7 -

A pension fund offers new customers, who deposit $1,000 a month until their retirement at the age of 67, a monthly interest rate of 0.5%. Assume the market's monthly interest rate is 0.327% (effective annual interest rate of 4%).

a) What will the account balance be on the 67th birthday of a customer who started depositing at the age of 47 (first payment deposited a month after his 47th birthday).

b) What is the present value of the investment in the pension fund for this customer (from the point of view of a 47 year old person)?

Mini-cases -

Overview to mini-cases

One of the best ways to understand interest calculations is to redo other peoples' examples.  In mini-cases we present a number of examples from the Web.  In each case students are asked to redo the calculations. 

In all of these cases the terminology annual percentage rate (APR) is used.  The concept of APR was designed to make it easier for borrowers to compare the cost of loans from different sources.  The Federal Truth in Lending Act requires lenders to disclose the APR, but unfortunately the Act does not specify how the APR is to be calculated.  

The result of this ambiguity is that there are many concepts of APR.   The message of Chapter 3 and of these cases is that the APR concept is not as meaningful as the effective annual interest rate (EAIR) for determining the actual cost of financing, the annualized internal rate of return of the loan payments.  Exhibit 1 shows a quote from the Cornell University Law Website which states the requirements for use of APR.

Exhibit 1:  Understanding The Law-When Should A Lender Disclose The Annual Percentage Rate (APR) and What Is It?

Mini-case 1:  MortgageRatesUSA.com

In the questions below, assume that you have taken a $100,000, 30-year mortgage with monthly payments:

1. What is the monthly payment on the mortgage?

2. What is the monthly interest rate that sets the NPV of the 360 monthly payments = 0?  [To answer this question you should use Excel's NPV function and Goal Seek.]

3. What is the effective annual interest rate on the mortgage? 

4. How did the authors of the Web page arrive at 8.107% APR?

Mini-case 2:  Columbia National gives a loan

The web page below gives a good definition of APR (and also shows why this concept is NOT a good finance concept!).  

This mini-case has 2 paragraphs. 

1. In paragraph 1:  Calculate:

• The monthly payments on the mortgage
• The monthly IRR (use PMT )
• Show that the APR in the paragraph = monthly IRR * 12 Compute the EAIR

2. In paragraph 2:

• Compute the monthly IRR, APR and EAIR for both loans (word of warning: the numbers on the Web page are slightly off). Which loan is preferable?

3. The Web page claims that loan 2 is preferable because the total payments over 60 months on this loan are lower than that on loan 1.  Show that this is wrong.

4. Despite its higher initial cost, you might think that loan 2 is preferable because it has a higher initial loan amount.  Calculate how much you would need to borrow with loan 1 in order to receive a net amount of $100,000 (you can do this calculation using Goal Seek, but it can also be done using the formulas of Chapter 2).  Doing it this way, show that Loan 1 is preferable.

Mini-Case 3:  Oregon Telco Credit Union

The Oregon Telco Credit Union has the following Web page:

Show that the Oregon Telco Credit Union's annual percentage rate (APR) is actually the effective annual interest rate (EAIR).

Need in Excel and each question should have different tab?.

Attachment:- Assignment File.rar