i. Define the annual percentage rate (APR). Suppose you borrow $3,621.15 and take out a loan with an 8% nominal interest rate. You must repay the loan with 48 monthly payments of $90 each. In addition, you must pay an initial loan processing fee of $100. What is the APR for this loan? j. Explain when you should use the: nominal rate (IOM), periodic rate (IPR), effective annual rate (EFF %), and annual percentage rate (APR). Can you think of a way to modify the APR so that it would be more helpful? If so, how would you calculate that rate? k. (1) Construct an amortization schedule for a $1,000, 10% annual rate loan with three equal installments. (2) During Year 2, what is the annual interest expense for the borrower, and what is the annual interest income for the lender? Hint: Construct an amortization schedule. 1. Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months (273 days) later? m. (1) Consider the time line shown here. Is the stream of cash flows an annuity? 0 100 2 100 3 Years H 100 (2) What is the value at the end of Year 3 of the previous cash flow stream if the quoted interest rate is 10%, compounded semiannually? (3) What is the PV of the same stream? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual com- pounding, when INOM EFF% IR) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM 2 -10%/25%? n. You have the chance to buy a guaranteed promissory note for $850. The note pays $1,000 in 15 months (i.e., exactly 456 days). You have $850 in a bank account that pays a 7% nominal rate compounded daily. Which is a better investment, the note or the bank account? Answer this question using three approaches: (1) compare your future value if you buy the note versus leaving your money in the bank; (2) compare the PV of the note with your current bank balance; and (3) compare the effective rate or return on the note with that of the bank account. Assume that you are nearing graduation and have applied for a job at a prestigious com- pany. The company's evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an or- dinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of Years 0 through 3. b. (1) What's the future value of an initial $100 after 3 years if it is invested in an ac- count paying 10% annual interest? (2) What's the present value of $100 to be received in 3 years if the appropriate inter- est rate is 10%? c. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% per year, how long will it take sales to double? d. If you want an investment to double in 3 years, what interest rate must it earn? c. What's the difference between an ordinary annuity and an annuity duc? What type of annuity is shown below? How would you change the time line to show the other type of annuity? 2 3 + H 100 100 100 g f. (1) What's the future value of a 3-year ordinary annuity of $100 if the appropriate interest rate is 10%? (2) What's the present value of the annuity? (3) What would the future and present values be if the annuity were an annuity duc? What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10%, compounded annually. 10% 2 3 + 0 100 300 300 -50 h. (1) Define the nominal rate (I), which also is called the stated rate and the quoted rate. Also define the periodic rate (1). If the nominal rate is 6% and is compounded quarterly, what is the periodic rate (1) If it is compounded monthly? PER (2) If the stated interest rate is constant, will the future value be larger or smaller if we compound an initial amount more often than annually (for example, semi- annually)? Why? (3) What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? (1) What is the effective annual rate (EFF %), also called the annual equivalent rate (AER)? What is the EFF % for a nominal rate of 12%, compounded semiannu- ally? Compounded quarterly? Compounded monthly? Compounded daily? (5) Can the effective annual rate ever be equal to the nominal (quoted) rate?

What is the maximum APR you can accept if you can afford to make monthly payments of $120 on a 7-year, $8000 loan?

What is the effective interest rate (APY) for a loan of $8,500 at 12% APR compounded monthly? use the formula method.

Consider a loan of $7700 at 6.8% compounded semiannually, with 18 semiannual payments. Find the following. (a) the payment necessary to amortize the loan (b) the total payments and the total amount of interest paid based on the calculated semiannual payments (c) the total payments and total amount of interest paid based upon an amortization table. (a) The semiannual payment needed to amortize this loan is $ (Round to the nearest cent as needed.) (b) The total amount of the payments is $ (Round to the nearest cent as needed.) The total amount of interest paid is $. (Round to the nearest cent as needed.) (c) The total payment for this loan from the amortization table is $ (Round to the nearest cent as needed.) The total interest from the amortization table is $ (Round to the nearest cent as needed.)

Consider a home mortgage of $125,000 at a fixed APR of 4.5% for 25 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest. ..... a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

The principal P is borrowed and the​ loan's future value A at time t is given. Determine the​ loan's simple interest rate r. P​ = ​$2300​, A​ = ​$2722​, t​ = 6 months.

TASK: 2 are mu pare Apply your understanding about the present value and future value of annuities and prepare TWO Loan EMI (EMI = Equated Monthly Installments) payment schedules based on the following instructions: 1. Loan Summary and schedule of Short term loan (20 marks) 2. Loan Summary and schedule of Long term loan (20 marks) Guidelines: 1. Suggested Short term Loan period is 1 year to 3 years 2. Suggested Long term Loan period is 7 years and above 3. Each loan summary should contains following points: a. What type of loan is chosen? b. Why it is chosen? C. Interest rate, number of years (loan period) and loan amount to be assumed and clearly stated d. Starting date and ending date of the loan period is to be mentioned 4. The payment schedule should cover the following: a. Serial No. b. Date (period) c. EMI amount (EMI = Equated Monthly Installments) d. Principal component of the EMI e. Interest component of the EMI f. Interest paid to date g. Principal paid- to date h. Principal…

G. Find the interest rate (APR) on a 27-year mortgage with a initial loan amount of $358,000, if the monthly payment is $2229.45 Let's use references for input values; and be sure to annualize the rate!                             INPUTS:   OUTPUT:               Period   Rate is   APR           Payment                   Loan amount

Find the APR of the loan given the amount of the loan, the number and type of payments, and the add-on interest rate. Loan amount, $9,000; three yearly payments; rate = 8% The annual percentage rate is%. (Type an integer or a decimal.)

Find the amount of interest and the maturity value of the following loan. Use the formula MV =P+I to find the maturity value. Round your answers to the nearest cent. Principal Rate (%) Time Interest Maturity Value $100,000 7 4 months