Fundamentals of Corporate Finance
11th Edition
ISBN: 9780077861704
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 6, Problem 62QP
Summary Introduction
To calculate: The interest rate of the loan
Introduction:
The EAR stands for the effective annual rate. The effective annual rate is the actual rate that is earned by an individual. The interest rates are generally shown as it were compounded once in a year.
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You are looking at a one-year loan of $20,000. The interest rate is quoted as 10 percent plus 2 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay 2 points to the lender up front and repay the loan later with 10 percent interest.
What rate would you actually be paying here?
You are looking at a one-year loan of $15,000. The interest rate is quoted as 10 percent plus 3 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay 3 points to the lender up front and repay the loan later with 10 percent interest.
What rate would you actually be paying here?
Multiple Choice
6.70%
10.00%
13.40%
12.06%
14.74%
You are looking at a one-year loan of $18,000. The interest rate is quoted as 7.4 percent
plus two points. A point on a loan is 1 percent (one percentage point) of the loan amount.
Quotes similar to this one are common with home mortgages. The interest rate quotation
in this example requires the borrower to pay two points to the lender up front and repay
the loan later with 7.4 percent interest.
a. What rate would you actually be paying here? (Do not round intermediate
calculations and enter your answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
b. What is the EAR for a one-year loan with a quoted interest rate of 10.4 percent plus
two points? (Do not round intermediate calculations and enter your answer as a
percent rounded to 2 decimal places, e.g., 32.16.)
a. Interest rate
b. EAR
9.41 %
10.61 %
Is your answer affected by the loan amount?
No
Yes
Chapter 6 Solutions
Fundamentals of Corporate Finance
Ch. 6.1 - Prob. 6.1ACQCh. 6.1 - Prob. 6.1BCQCh. 6.1 - Unless we are explicitly told otherwise, what do...Ch. 6.2 - In general, what is the present value of an...Ch. 6.2 - In general, what is the present value of a...Ch. 6.3 - If an interest rate is given as 12 percent...Ch. 6.3 - What is an APR? What is an EAR? Are they the same...Ch. 6.3 - Prob. 6.3CCQCh. 6.3 - What does continuous compounding mean?Ch. 6.4 - What is a pure discount loan? An interest-only...
Ch. 6.4 - What does it mean to amortize a loan?Ch. 6.4 - Prob. 6.4CCQCh. 6 - Two years ago, you opened an investment account...Ch. 6 - A stream of equal payments that occur at the...Ch. 6 - Your credit card charges interest of 1.2 percent...Ch. 6 - What type of loan is repaid in a single lump sum?Ch. 6 - Annuity Factors [LO1] There are four pieces to an...Ch. 6 - Prob. 2CRCTCh. 6 - Prob. 3CRCTCh. 6 - Present Value [LO1] What do you think about the...Ch. 6 - Prob. 5CRCTCh. 6 - Prob. 6CRCTCh. 6 - APR and EAR [LO4] Should lending laws be changed...Ch. 6 - Prob. 8CRCTCh. 6 - Prob. 9CRCTCh. 6 - Prob. 10CRCTCh. 6 - Prob. 11CRCTCh. 6 - Prob. 12CRCTCh. 6 - Prob. 1QPCh. 6 - Prob. 2QPCh. 6 - Prob. 3QPCh. 6 - Prob. 4QPCh. 6 - Calculating Annuity Cash Flows [LO1] If you put up...Ch. 6 - Calculating Annuity Values [LO1] Your company will...Ch. 6 - Calculating Annuity Values [LO1] If you deposit...Ch. 6 - Calculating Annuity Values [LO1] You want to have...Ch. 6 - Prob. 9QPCh. 6 - Calculating Perpetuity Values [LO1] The Maybe Pay...Ch. 6 - Prob. 11QPCh. 6 - Prob. 12QPCh. 6 - Calculating APR [LO4] Find the APR, or stated...Ch. 6 - Calculating EAR [LO4] First National Bank charges...Ch. 6 - Prob. 15QPCh. 6 - Prob. 16QPCh. 6 - Prob. 17QPCh. 6 - Calculating Present Values [LO1] An investment...Ch. 6 - EAR versus APR [LO4] Big Doms Pawn Shop charges an...Ch. 6 - Prob. 20QPCh. 6 - Calculating Number of Periods [LO3] One of your...Ch. 6 - Calculating EAR [LO4] Friendlys Quick Loans, Inc.,...Ch. 6 - Prob. 23QPCh. 6 - Calculating Annuity Future Values [LO1] You are...Ch. 6 - Calculating Annuity Future Values [LO1] In the...Ch. 6 - Prob. 26QPCh. 6 - Prob. 27QPCh. 6 - Prob. 28QPCh. 6 - Simple Interest versus Compound Interest [LO4]...Ch. 6 - Prob. 30QPCh. 6 - Prob. 31QPCh. 6 - Prob. 32QPCh. 6 - Calculating Future Values [LO1] You have an...Ch. 6 - Calculating Annuity Payments [LO1] You want to be...Ch. 6 - Prob. 35QPCh. 6 - Prob. 36QPCh. 6 - Prob. 37QPCh. 6 - Growing Annuity [LO1] Your job pays you only once...Ch. 6 - Prob. 39QPCh. 6 - Calculating the Number of Payments [LO2] Youre...Ch. 6 - Prob. 41QPCh. 6 - Prob. 42QPCh. 6 - Prob. 43QPCh. 6 - Prob. 44QPCh. 6 - Prob. 45QPCh. 6 - Prob. 46QPCh. 6 - Prob. 47QPCh. 6 - Prob. 48QPCh. 6 - Prob. 49QPCh. 6 - Calculating Present Value of a Perpetuity [LO1]...Ch. 6 - Prob. 51QPCh. 6 - Prob. 52QPCh. 6 - Calculating Annuities Due [LO1] Suppose you are...Ch. 6 - Prob. 54QPCh. 6 - Prob. 55QPCh. 6 - Prob. 56QPCh. 6 - Prob. 57QPCh. 6 - Prob. 58QPCh. 6 - Prob. 59QPCh. 6 - Prob. 60QPCh. 6 - Calculating Annuity Values [LO1] You are serving...Ch. 6 - Prob. 62QPCh. 6 - Calculating EAR with Points [LO4] The interest...Ch. 6 - Prob. 64QPCh. 6 - Prob. 65QPCh. 6 - Prob. 66QPCh. 6 - Prob. 67QPCh. 6 - Calculating Annuity Payments [LO1] This is a...Ch. 6 - Prob. 69QPCh. 6 - Prob. 70QPCh. 6 - Prob. 71QPCh. 6 - Calculating Interest Rates [LO4] A financial...Ch. 6 - Prob. 73QPCh. 6 - Prob. 74QPCh. 6 - Ordinary Annuities and Annuities Due [LO1] As...Ch. 6 - Calculating Growing Annuities [LO1] You have 40...Ch. 6 - Prob. 77QPCh. 6 - Prob. 78QPCh. 6 - Prob. 79QPCh. 6 - Prob. 80QPCh. 6 - Prob. 1MCh. 6 - Prob. 2MCh. 6 - Prob. 3MCh. 6 - Prob. 4MCh. 6 - Prob. 5MCh. 6 - Prob. 6M
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- Nonearrow_forwardYou are looking at a one-year loan of $10,000. The Interest rate is quoted as 9.7 percent plus two points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The Interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 9.7 percent Interest. What rate would you actually be paying here? Note: Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. Interest rate %arrow_forwardIn a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as $34,000 and the interest rate is 9.50%, the borrower “pays” 0.0950 × $34,000 = $3,230 immediately, thereby receiving net funds of $30,770 and repaying $34,000 in a year. A. What is the effective interest rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) B. What is the effective annual rate on a 1-year loan with an interest rate quoted on a discount basis of 19.50%? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)arrow_forward
- You are looking at a one-year loan of $20,000. The interest rate is quoted as 10 percent plus two points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 10 percent interest. What rate would you actually be paying here? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. Answer is complete but not entirely correct. Interest rate 12:00 %arrow_forward14. In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as $10,000 and the interest rate is 10%, the borrower "pays" .10 × $10,000 = $1,000 immediately, thereby receiving net funds of $9,000 and repaying $10,000 in a year. a. What is the effective interest rate on this loan? (Round your answer to 2 decimal places.) b. If you call the discount d (for example, d = 10% using our numbers), express the effective annual rate on the loan as a function of d. c. Is the effective annual rate always greater than the stated rate d?arrow_forwardRadhubhaiarrow_forward
- 4. If you know the simple interest due on a P10 000 loan, explain how you can use that figure to calculate the simple interest due on a P50 000 loan for the same time period and the same interest rate. 5. If the principal of a loan is doubled but the time period and interest rate remain the same, how many times as large is the simple interest due on the loan? 6. If the principal of a loan is tripled but the time period and interest rate remain the same, how many times as large is the simple interest due on the loan?arrow_forwardConsider a borrower who took a loan worth 10000 at the beginning of period 1. The loan is to be repaid over 20 periods. Furthermore, assume that the interest rate is equal to 5%. How much does the borrower owe in debt at the beginning of period 3? Don't use Excelarrow_forwardYou are looking at a one-year loan of $12,500. The interest rate is quoted as 9.5 percent plus four points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay four points to the lender up front and repay the loan later with 9.5 percent interest. What rate would you actually be paying here?arrow_forward
- Suppose you take out a home mortgage for $160,000 at a monthly interest rate of 0.6%. If you make payments of $1200/month, after how many months will the loan balance be zero? Estimate the answer by graphing the sequence of loan balances and then obtain an exact answer. Graph the sequence of loan balances. Choose the correct graph below. O A. 160,000 its 125 months loan balance 150 Q Q The loan balance will be zero after 269 months. (Round up to the nearest month.) O B. loan balance 160,000 125 150 months Q O loan balance 160,000 260 290 months Q O D. 160,000 it loan balance 260 ¹290 months Ⓒ Qarrow_forwardSuppose that you have two loan choices with monthly payments Choice Loan Amount Term (years) Interest Rate 1 $ 250,000 30 5% 2 $ 220,000 30 4.50% (a) What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you hold the loan for the entire term and there are no origination costs for the two loans? Incremental Borrowing Cost: $3,254.72 (b) What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you hold the loan for only 6 years (72 months) and there are no origination costs for the two loans? Incremental Borrowing Cost: $650.94arrow_forward2. Problem 5.17 (Effective Interest Rate) еВook You borrow $225,000; the annual loan payments are $30,017.40 for 30 years. What interest rate are you being charged? Round your answer to the nearest whole number. %arrow_forward
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