Lecture 5 - Lecture 5 Loans and Costs of Borrowing 1 Loan balance prospective method and retrospective method Amortization schedule Sinking fund Varying

# Lecture 5 - Lecture 5 Loans and Costs of Borrowing 1 Loan...

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Lecture 5 Loans and Costs of Borrowing 1
Loan balance: prospective method and retrospective method Amortization schedule Sinking fund Varying installments and varying interest rates Quoted rate of interest and equivalent nominal rate of interest in monthly rest Flat rate loan and flat rate discount loan Annual percentage rate, annual percentage yield, effective rate of interest, and comparison rate of interest 2
Consider a loan with a fixed term of maturity, to be redeemed by a series of repayments. If the repayments prior to maturity are only to offset the interests, the loan is called an interest-only loan. If the repayments include both payment of interest and partial redemption of the principal, the loan is called a repayment loan. We consider two approaches to compute the balance of the loan: the prospective method and the retrospective method. 3
The prospective method is forward looking. It calculates the loan balance as the present value of all future payments to be made. The retrospective method is backward looking. It calculates the loan balance as the accumulated value of the loan at the time of evaluation minus the accumulated value of all installments paid up to the time of evaluation. 4
Example: A housing loan of \$400,000 was to be repaid over 20 years by monthly installments of an Ordinary annuity at the nominal rate of 5% per year. After the 24th payment was made, the bank increased the interest rate to 5.5%. If the lender was required to repay the loan within the same period, how much would be the increase in the monthly installment. If the installment remained unchanged, how much longer would it take to pay back the loan? 5
Ordinary Annuity Part (a) Initial payment was: C=?; where PVA = 400 000; k=0.05/12: n=20*12=240 C=\$2639.82 Amount that needs to be paid after the increase in rates: PVA=? Where k=0.05/12; n=240-24=216 PVA=\$375 489.74 6
Payment amount after the increase in interest C=?; where PVA = 375 489.74; k=0.055/12: n=216 C=\$2742.26 so that the increase in installment is \$2742.26-\$2639.82 = 102.44 7
Part (b) If the installment remained unchanged, you have to calculate n, where PVA =375489.74; c=\$2639.82: k=0.055/12 using: You will get n=231 So additional months is: 231-216 = 15 months 8
Example :

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