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8. A bank provides a loan product with loan amount L. The loan is to be repaid over n years with increasing annual instalments payable

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8. A bank provides a loan product with loan amount L. The loan is to be repaid over n years with increasing annual instalments payable in arrears. (a) Assume that the instalments increases every year at the rate of g per annum and the bank requires an effective rate of return of i per annum, where i=g. If the first instalment is denoted by X, show that L=X(ig1(1+i1+g)n) [7 marks] (b) A company has borrowed 150,000 from the bank and agreed to repay the loan over 12 years with increasing annual instalments in arrears that grows at rate of 7% per annum. (i) Calculate the amount of the first instalment if the bank requires an effective yield of 10%. [2 marks] (ii) For each of the year 10 and year 11, construct a loan schedule showing the outstanding capital at the beginning of the year, the interest payment and the capital payment. [9 marks] [Total: 18 marks] 8. A bank provides a loan product with loan amount L. The loan is to be repaid over n years with increasing annual instalments payable in arrears. (a) Assume that the instalments increases every year at the rate of g per annum and the bank requires an effective rate of return of i per annum, where i=g. If the first instalment is denoted by X, show that L=X(ig1(1+i1+g)n) [7 marks] (b) A company has borrowed 150,000 from the bank and agreed to repay the loan over 12 years with increasing annual instalments in arrears that grows at rate of 7% per annum. (i) Calculate the amount of the first instalment if the bank requires an effective yield of 10%. [2 marks] (ii) For each of the year 10 and year 11, construct a loan schedule showing the outstanding capital at the beginning of the year, the interest payment and the capital payment. [9 marks] [Total: 18 marks]

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