B4. (a) One beerows f 150.000 from a bank bo buy an apurm -sies fepayments offDp

Question

B4. (a) One beerows f 150.000 from a bank bo buy an apurm -sies fepayments offDpef month. The bank charges a sominal anual iteres rate ef 60cepounded mony The balance that owed to the bank (in pounds) at the end ofm is given by where J-1 + r/100, E, is the initial loan in pounds), r% is. mnthly interest rate. (i) Assume that the monthly repayment is D-100·sh e fr p and tootuin an espression for B, in tems of Use you formola to answer the following question After how many months will the loan be paid of . The payment in the final month will be less thn 0o0 Cakculate how much it should be. What will the total repayment he? Give the answers in pounds to two decimal places i) What should be the minimall monthly repayment for the loan to be paid of within 2 years? Givehe answers in pounds, to two decimal places

Explanation / Answer

Requirement (i) BN will be 0 because entire loan would have repaid by then BN 0 =PN*150000-((PN-1)/(P-1))*1000 0 =150000PN-((PN-1)/0.005)*1000 0 =150000PN-(1000PN-1000)/0.005 0 =PN150000-PN200000+200000 PN   = 0.25 Present value factor for 0.5% interest at 278 month comes to 0.25 So loan will be repaid in 278 months In the final Month we will pay 950 to arrive at perfect repayment of principal amount of 150000 The total repayment will be 277950 Requirement (ii) The Minimal monthly repayment for the loan to be repaid within 25 years is The annuity factor at 0.5% for 300 period ( 25Years ) is                  = 155.206864 So,   its =150000/155.206864 Minimal Monthly payment        = 966.452102

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