(i) A government is holding an inquiry into the provision of loans by microfinance institutions (MFIs) to consumers at high rates of interest. The loans are typically of short duration and to high risk consumers. Repayments are collected in person by representatives of the MFIs making the loan. Campaigners on behalf of the consumers and campaigners on behalf of the MFIs granting the loans are disputing one particular type of loan. The initial loans are for K2,000. Repayments are made at an annual rate of K2,400 payable monthly in advance for two years.

The consumers association case

The consumers association asserts that, on this particular type of loan, consumers who make all their repayments pay interest at an annual effective rate of over 200%.

The MFIs case

The MFIs state that, on the same loans, 40% of the consumers default on all their remaining payments after exactly 12 payments have been made. Furthermore half of the consumers who have not defaulted after 12 payments default on all their remaining payments after exactly 18 payments have been made. The MFIs also argue that it costs 30% of each monthly repayment to collect the payment. These costs are still incurred even if the payment is not made by the consumer. Furthermore, with inflation of above 2.5% per annum, the MFIs therefore assert that the real rate of interest that the lender obtains on the loan is less than 1.463% per annum effective.

(a) Describe the impact of any three determinants of interest rates implied from the MFIs case. [3 marks]

(b) Show that any one of the the above presentations by the ANY of the two sides is fairly correct. [2 marks]

(c) Use the distinction between different types of interest rates to arbitrate between the two parties. [4 marks]

(ii) Calculate the time it takes for K3,600 to accumulate to K4,000 at:

(a) a simple rate of interest of 6% per annum [1 marks]

(b) a compound rate of interest of 6% per annum convertible half yearly [2 marks]

(iii) A company has borrowed K800,000 from a bank. The loan is to be repaid by level installments, payable annually in arrears for 10 years from the date the loan is made.

The annual repayments are calculated at an effective rate of interest of 8% per annum.

(a) Calculate the amount of the level annual payment which will be paid over the 10 year term. [3 marks]

(b) Construct an amortisation schedule showing the capital and interest components over the entire life of the loan. [5 marks]