chapter 5 fina 3332

•Yield Curve

-A plot of bond yields as a function of the bonds' maturity date

•Term Structure

-The relationship between the investment term and the interest rate

effective annual rate

-Total amount of interest earned in one year §The annual rate of actual interest earned §Includes the effects of compounded interest -Used to compare returns on investments (or loans) with different compounding of interest per year.

In 2007, interest rates were about 4.8% and inflation was about 2.5%. What was the real interest rate in 2007?

2.24

learning cat A home buyer buys a house for $150,000. She pays 20% cash, and takes a fixed-rate mortgage for ten years at 4.50% APR. If she makes semi-monthly payments, which of the following is closest to each of her payment?

240=n 1200000= pv i/y= 4.5/24 because semi monthly fv= 0 pmt= 621.37

learning cat Consider the timeline for a $30,000 car loan with these terms: 6.75% APR for 60 months. What is your monthly payment?

590.5

If the current inflation rate is 3.0%, then the nominal rate necessary for you to earn a(n) 5.4% real interest rate on your investment is closest to ________

8.56 rearrange equation

Higher supply (lending)

=> lower the interest rate

•Stern deposits a fixed amount monthly in a bank account with an EAR of 10.5%. What is the APR?

APR=(1+EAR)^(1⁄m)-1]×m APR=〖[(1.105)〗^(1⁄12)-1]×12=10.0262%

Five years ago you took out a 30-year mortgage with an APR of 6.20% for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95%, how much would your new loan payment?

Current Mortgage Payment: N =12* 30 years = 360, I/Y =6.20/12 = 0.51667%, PV = $206,000 PMT = 1261.69 Current Mortgage Balance: N = 12* (30 Years - 5 Years) = 300, I/Y =6.20/12 = 0.51667%, PMT = 1261.69, Solve for PV = $192,159.69 New Mortgage Payment: N = 240, I/Y = 3.95/12 = 0.32917%, PV = $192,159.69 Solve for PMT = $1159.39

3 types of loans

Pure Discount Interest Only Amortized

You have just sold your house for $1,000,000 in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 6.25% ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

calculate orignal mortgage payment n=30x12= 360 i/y= 6.25/12=.5208 pv=800000 fv=0 pmt= 4,925.5295 now with the pmt, compute how much left is to to pay (PV) just change n to the remaining time to pay (30-18.5) x 12= 138 pv= 483,952.8205 it asks how much cash you have left so, 1,000,000- 483,952.8205= 516047.17 close enough to answer on catalytics

Let's say that you are now 10 years into a $200,000 mortgage (at 4.80% APR, originally for 360 months), and you decide to sell the house. When you sell the house, you will need to pay whatever the remaining balance is on your mortgage. After 120 months of payments, how much do you still owe on your mortgage?

calculate the pmt for the orignal mortgage n= 360 i/y=.40 pv= 200000 fv=0 pmt= 1049.3307 now compute present value of the remaining 240 months n=240 i/t= .4 pmt= 1049.3307 fv=0 pv= 161,695

Five years ago you took out a 30-year mortgage with an APR of 6.20% for $206,000. How much do you still owe on your mortgage?

calculate the pmt for the orignal mortgage n=30x12=360 i/y= 6.2/12= .5167 pv= 206000 fv=0 pmt= 1261.6861 now compute present value of the remaining mortgage balacne n=25x12=300 i/y= .5167 pmt= 1261.6861 fv=0 pv= $192,159.69

Consider the following investment alternatives: Investment APR Comp. A 6. 2830% Annual B 6.1116% Daily C 6.1834% Quarterly D 6.1744% Monthly The highest effective rate of return you could earn on any of these investments is the one with the ________compounding.

formula is ear= (1/ APR/m)^m -1 the annual rate is already solved

•At the start of 2008, one-year U.S. government bond rates were about 3.3%, while the inflation rate that year was 0.1%. At the start of 2018, one-year interest rates were about 1.8%, and the inflation rate that year was about 1.9%. What were the real interest rates in 2008 and in 2018?

formula= 1+ rreal interest rate= 1+ nominal interest rate/ 1 + inflation rate in 2008- 1.033/1.001 -1 = 3.2 same for 2018

Higher demand (borrowing)

higher the interest rate

Suppose your bank account pays interest monthly with an effective annual rate of 5%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $150,000 in 20 years?

multiply by 100 1.05 - yx in calculator - 12 - 1/x - = - -1 then multiply by 100 then use the rate in calculator and put other values

A house costs $115,000. It is to be paid off in exactly ten years, with monthly payments of $1424.50. What is the APR of this loan?

solve for interest rate in calc then multiply by 12

learning catalytics Your firm is purchasing a new fleet of trucks that will last for six years. You can purchase the system for an upfront cost of $500,000 or lease the system from the manufacturer for $8,000, paid at the end of each month for a 72-month. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase paying upfront or lease?

solve for pv and put - for pmt

•Your firm is purchasing a new telephone system that will last for four years. You can purchase the system for an up-front cost of $150,000 or lease the system from the manufacturer for $4,000, paid at the end of each month. The lease price is offered for a 48-month lease. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright or pay $4000 per month?

solve for pv first

nominal interest rate

§The rate at which your money will grow if invested for a certain period

-Real Interest Rate

§The rate of growth of your purchasing power, after adjusting for inflation

what is interest rate

•Interest rates are the price of using money. -Rental price for money -Cost to borrowers for consuming before earning -Reward to savers for postponing consumption

•Let's say that you are three years into your $30,000 car loan from the previous section and decide to sell the car. When you sell the car, you must pay whatever the remaining balance is on your car loan. After 36 months of payments at $590.50, how much do you still owe on your car loan? •Interest rate 6.75% APR, compounded monthly

•The remaining balance on your loan is the PV of the remaining 24 monthly payments of $590.50. n=24 i/y= .5625 pmt= 590.50 fv= 0 pv= 13222.32