BMGT340 Class Notes Ch 05 Pt 1

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Jan 9, 2024

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Business Finance – Chapter 5 Part 1 Interest Rate Topics: Effective Annual Rate (EAR) and Loan Amortization I. Effective Annual Rate (EAR) vs. Annual Percentage Rate (APR) a. Formulas: i. Periodic Rate: r = APR/m ii. EAR = (1+r) m – 1 b. What is the purpose of the EAR? APR? c. Learning Catalytics Problems i. LC#12 Three banks offer these rates and compounding frequencies on their savings accounts: Ritchie Bank: 8.00% APR compounded daily (365 days/year) Cole Bank: 8.05% APR compounded quarterly Byrd Bank: 8.03% APR compounded monthly Which offers the best savings account? What is its effective annual rate (EAR)? Choose the higher one Byrd Bank EAR. = (1+.0803/12)^12 - 1 ii. LC#13 Alpha National Bank charges 9% interest compounded quarterly on its business loans. Beta State Bank charges 9.10% interest compounded semiannually on its business loans. As a potential borrower, which bank would borrow from? What effective annual rate will you pay? Borrowing so you choose the smaller answer Alpha National Bank: EAR= (1+.09/4)^4 -1 iii. LC#3 Suppose your bank account pays interest monthly with an effective annual rate of 6%. If you have no money in the bank
today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years? 0.6=(1+r)^12 – 1 R= 0.00486755057 Annuity so put it into calculator. = 615.49 iv. LC#2 The effective annual rate of a certificate of deposit that compounds daily is 8.3278%. Assume 365 days per year. What is the APR? Periodic Rate: r = APR/m EAR = (1+r) m – 1 Use those two equatons M =365 EAR=8.3278% r=(1+EAR)^(1/m) – 1 APR=r * m 8.00% v. You buy a security that pays $500 every 6 months for 10 years. Another security with the same risk will also mature in 10 years and pays 10% APR, compounded monthly. What should be the price of the security you just bought? r=APR/m = .1/12 E(6mo)R= (1+r)^6 -1 0.05105333
Use E(6mo)R as r in annuity formula. 20 periods, 500/period 6175.83
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vi. You buy a security that pays $100/quarter for 10 years. Another security with the same risk will also mature in 10 years and pays 16% interest compounded monthly. What should be the price of the security you just bought? vii. Plaza Gold Emporium wants to sell on credit, giving customers 4 months to pay. However, the firm will have to borrow from its bank to carry the A/R. The bank will charge 18%, compounded monthly. The firm wants to quote a nominal rate to its customers, all of whom are expected to pay at the end of 4 months that will exactly cover its financing costs. What nominal annual rate should Plaza quote to its credit customers? viii. Charlotte is a wealthy investor in start-up businesses. She typically lends at 24% APR with monthly compounding. The owner of HB Enterprises approaches her for a loan that HB will pay back in quarterly installments of $4,000 over 8 years. What is the most Charlotte should lend to HB Enterprises? a. $50,736 b. $55,587 c. $56,336 d. $54,740 e. $60,527
II. Loan Amortization a. Breakdown of a Loan Payment: i. Interest Portion of Loan Payment = Loan Balance at Beginning of Period * r ii. Principal Portion of Loan Payment = PMT – Interest Portion b. Trick: Given a number or periods remaining in a loan, you can find the outstanding loan balance by taking the present value of all remaining payments. c. LC#6 You have a loan of $25,000 and will repay the loan with monthly payments over 5 years at 8% interest compounded monthly. What is your loan payment? After you have made the first 24 payments, how much is the outstanding principal balance on this loan? d. LC#7 You take out a mortgage for 400,000 USD at an APR of 6%. The mortgage lasts for 360 months (30 years). How much will you still owe on this mortgage after making payments for 120 months (10 years)?
e. Follow-up: You take out a mortgage for 400,000 USD at an APR of 6%. The mortgage lasts for 360 months (30 years). How much of the 121 st payment is the principal portion? f. LC#15 Adele took out a 30 year $400,000 mortgage 12 years ago at an APR of 6% with monthly payments. She wishes to refinance her mortgage into one with an APR of 4% and maturity of 15 years. What would her monthly payments be if she refinances? g. Exam Questions i. You are considering a mortgage for $500,000 that requires a monthly payment of $2,500 per month or 30 years (360 months) and an upfront payment of $5,000 (also called a "point" or a loan origination fee) at the time of taking out the loan. What effective annual rate will you pay on this mortgage after taking into consideration the upfront fee? A. 4.48% B. 6.23% C. 4.57% D. 6.00% E. 4.39%
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ii. Amos took out a $20,000 60 month car loan 12 months ago. His monthly payment is $375.59. What is the outstanding balance on this loan? A. $18,028 B. $11,261 C. $15,238 D. $4,392 E. $16,374