1 第七章 貸款條件與貸款利率 Loan Interest Rates and Repayment Term

2 Factors Affecting the Cost of Credit Interest rate: cost of funds risk premium loan administrations and servecing costs inflation Simple and Compound interest terminology exact simple interest (365/366 days) Simple interest ordinary simple interest (360 days) Compound interest － the interest is periodically converted to principal conversion period principal + compound interest = compound amount

3 p.133 Table 7.1 conversion period: annually, semiannually, quarterly Compound rate = True rate = Actuarial rate － rate per conversion period (8%, 4%, 2%) Effective annual rate (8%, 8.16%, 8.243%) Nominal rate (8%, 8%, 8%)

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5 Loan payment plans: “Amortized Loan”: Loan repaid in a series of payments that cover interest and principal. “Nonamortized loans” call for payment of the entire principal amount on the expiration of the term of the loan － regular scheduled payments of interest. “Partially amortized loan” is one that calls for small principal payments each year during the repayment term of the loan, with the unpaid balance of the principal due as a lump sum or “balloon payment” at the end of the term. ( p.135 ) balloon payment ： $50,000 + $2,500 + $4,725 ( unpaid principal ) ( perial principal ) ( interest for the 20th period) amortization = installments 分期攤還

6 Methods of Computing Loan Payments a. decreasing payment A. Interest on Unpaid Balance b. level payment B. Interest on Beginning Balance a. discount method b. add-on method p.136 Table 7.2

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8 A. Interest on unpaid balance a. annual level payment = principal × Table 3 b. decreasing payment = principal / n + 利息 B. Interest on beginning balance a. discount method : $1,000, 7%, 3years 0.07 × 3 × $1000 = $210 the borrowing actually receive only $790 $1,000 / 36 = $27.78 b. Add-on interest method : 3 yrs, 7%, $1,000 loan interest : $210 receive : $1,000 monthly payment : ($1000+$210)/36=$33.61 Flexible or variable payment loans ： －貸款利息或本金的償還隨著作物產量、價格或所得而變動 （固定） （遞減） the total interest charges are discounted from the beginning principal amount 附加利息

9 Computing Interest rates I. Stelson equation Nominal interest rate = example: $1,000, 7% add-on loan repayable in36 monthly payments beginning principal (B) = $1,000 total number of payment (n) = 36 number of payment per year (m) = 12term of loan in years (t) = 3 amount of interest (I) = 210amount of each periodic payment (a) = 1210 ÷ 36 = add-on:, discount method:

10 add-on discount Effects of Loan Term and Repayment Schedule for both add-on and discounted installment loan, the nominal rate exceed the quoted rate. Usually, loan term↑nominal rate↑ payment interval↓nominal rate↑ (number of payment per year↓) example: Table 7.4, p.143 II. Direct ratio equation 直接比率

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12  提前付清餘款時 : $3,000, 8%, 36 month, add-on, 第 21 month 付清, 付 ? $3,000 × 0.08 × 3 = $720 ($3,000 + $720) ÷ 36 = $ $ × (36-20) - $720 ×= $ Discount for customers who pay within a certain time following the billing date (interest charge for accounts outstanding beyond the due date) : “2/10/net 30” means: 2% discount if the account is paid within 10 days, otherwise the balance is due in full within 30 days

13  A customer who passed up the discount when the terms are “2/10/net 30” would be paying a rate of approximately 37.2% $100 × 2% = $2 $2 ÷ ($100-$2) = 2.04% 2.04% × 365 ÷ (30-10) = 37.2%  年保費 100 元 半年支付 52 元 52 × 2 –100 = – 52 = 48 4 ÷ (100-52) = 8.33% 52 – 48 = 4 ( p.145 ) 8.33% × 12 ÷ 6 = 16.67% (4 ÷ 48)×(12 ÷ 6) = 16.67%