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Kiki has returned to her office at Mercury Bank, and sees some loan case files have been left for her to review. All loans at Mercury Bank charge a fixed interest rate (i.e. it does not change over the life of the loan), but different loans can have different interest rates charged.

She reads through these case files and notes the following interesting cases:

Case 1:

A loan of $473,000 was made with a term of 30 years. There are level monthly repayments of $21845.033907, but the interest rate being charged on the loan is not known.

Calculate the interest rate for this loan, expressed as an effective monthly rate. Give your answer as a percentage, to 4 decimal places. (1 mark)

Case 2:

A loan was made to a customer some time ago, but there are no records of when this occurred, or the original loan amount.

All that is known is that exactly one year ago, the loan outstanding was $635,000, there were level monthly repayments of $21612.226011 (the most recent payment being made today), and the loan outstanding today is $439,000 (after taking into account the payment made today).

Calculate the interest rate for this loan, expressed as a nominal annual rate compounding monthly. Give your answer as a percentage, to 4 decimal places. (1 mark)

Case 3:

A loan of $391,000 was made today by a new customer. The customer has decided to make quarterly repayments of $20527 at the start of each quarter for the forseeable future.

After 1 year, the loan outstanding turns out to be $386030.493926 (note that only 4 repayments are made).

Calculate the interest rate for this loan, expressed as a nominal annual rate compounding quarterly. Give your answer as a percentage, to 4 decimal places. (1mark)

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