You have just passed ACST1001 and started a summer internship at Harrison Bank, with Peter as your supervisor. As your first task, Peter has given you some client accounts and asked you to verify some of the details.

The first file is for a client named Mary, who has a mortgage with the bank. You go through the file and note the following information for Marys mortgage

• Initial loan: $650,000
• Term of loan: 20 years
• Repayment frequency: End of each fortnight
• Interest rate on loan: 12=i12=3.1%

Using this information, determine the following:

1. What is the periodicity needed given the above information?

a. Monthly, since the 3.1% is a nominal annual rate compounding monthly

b. Daily, since there are exactly 365 days in a year (ignoring leap years)

c. Yearly, since the term of the loan is measured in years

d. Fortnightly, since the repayments are fortnightly

2. The interest rate for Mary's loan is 12=i12=3.1%. Calculate the effective monthly rate. Give your answer as a percentage to 4 decimal places, and do NOT include a percentage sign.

3. Calculate the effective fortnightly rate. Give your answer as a percentage to 4 decimal places, and do NOT include a percentage sign

4. Calculate the size of each of Marys repayments using the information given above. Give your answer to the nearest cent, and do NOT include a dollar sign.

5. The second file is for a client named Toomes, who also has a mortgage with the bank. The details you can gather for Toomes loan are as follows:

• Current loan outstanding: $630,000
• Current monthly repayment: $2050
• Next repayment: Due exactly 1 month from now
• Interest rate on loan: 12=i12=2.5%

Using this information, determine the following:

How much interest is Toomes charged for the coming month? Do NOT include a dollar sign in your answer.

6. What will be Toomes loan outstanding after 1 month, immediately after the payment due on that day? Do NOT include a dollar sign in your answer.

7. What is the loan outstanding after 1 year? Give your answer to the nearest cent, and do NOT include a dollar sign.

8. The third file is for a client named Alexei. Alexei took out a personal loan exactly one year ago with Harrison Bank. From his file, you have noted the following information:

• Original loan amount: $37,000
• Current loan outstanding: $31144.39
• Monthly repayment: $760
• Next repayment: Due exactly 1 month from now
• Interest rate on loan:12i12=9.5%

For the purposes of the remaining questions, use the rounded values given above. Using this information, determine the following:

How much principal has Alexei repaid over the last year? Give your answer to the nearest cent, and do NOT include a dollar sign.

9. How much interest has Alexei been charged over the past year? Give your answer to the nearest cent, and do NOT include a dollar sign.

10. If Alexei continues making monthly repayments of $760, and if the interest rate does not change, how many further FULL repayments does he expect to have to make in order to repay the loan? Do NOT include any final smaller repayment to pay off the remaining balance.