Finance 1, 1st test

Yield to Maturity of a Coupon Bond Consider the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons described in the previous example. If this bond is currently trading for a price of $963.11, what is the bond's yield to maturity? *The YTM y we find is for 6-months (the basis of the 10 payments periods), how do we make it an annual rate?

2.2 x $1,000=$22/2=11 Solution keys: N=10 I/YR= ? 1.5%(solve) PV=-963.11 PMT=11 FV=1,000

consider a 10-year bond with a face value of $1,000 that has a coupon rate 5.2%, with semiannual payments. what is the coupon payment for this bond?

CPN=(Coupon rate x face value)/# of coupon payments per year

suppose your currently have $5,100 in your savings account, and your bank pays interest at a rate of .54% per month. If you make no further deposits or withdrawals, how much will you have in the account in 4 years?

FV=C×(1+r)^N or N=48 I/YR=.54% PV=$5,100 FV=?

suppose bank is offering a 30-year mortgage with an EAR of 5.625%. If you plan to borrow $220,000, what will be your monthly payment?

I/YR=.4571 N=360 PV=220,000 PMT=?1247.1

you figure that the total cost of college will be $110,000 per year 18 years from today. if your discount rate is 13% compounded annually, what is the present value today of four of college costs starting 18 years from today?

N=4 I/YR=13% PMT=110,000 PV=? 327,191.85 then N=17 I/YR=13% FV=327,191.85 PV=?(40,970.28)

suppose a five year, $1,000 bond with annual coupons has a price of $899.94 and a yield to maturity of 6.3%. what is the bonds coupon rate?

N=Years I/YR=yield of maturity PV=-coupon price FV=bond PMT=? move 1 decimal to the left

What is the future value of your windmill in three years?

PV(1plusR)^n

a rich aunt has promised you $7,000 one year from today. in addition, each year after that, she has promised you a payment( on the anniversary of the last payment) that is 7% larger than the last payment. she will continue to show this generosity for 20 years, giving a total of 20 payments. if the interest rate is 10%, What is her promise worth today

PV= C/(r-g)×(1-((1+g)/(1+r))^N ) * do it step by step

you want to endow a scholarship that will pay $10,000 per year forever. If the schools endowment rate is 7%, what amount must you donate to endow the scholarship? How would your answer change if you endow it now, but it makes the first award to a student 10 years from today?

PV=C/r Where C= Cash flow & r=discount rate(input percentage as decimal) (PV)/(1+r)^x-1 where x = years discounted

A local Bank is running th following advertisement in the newspaper:"for just $6,000 we will pay you $450 forever!" The fine print in the ad says that for a $6,000 deposit, the bank will pay$450 in perpetuity, starting 1 year after the deposit has been made.what interest rate is the bank advertising (what is the rate of return on the investment)?

PV=C/r = r=C450/PV6000

APR vs EAR Find the EAR of an 18% APR loan compounded monthly

Solution Keys 12 Orange Shift P/YR 18 Orange Shift NOM% Orange Shift EFF%

Monthly Payments You borrow $150,000 today for a 15 year mortgage. The interest rate is 10% and you need to make monthly payments. Find the payment.

Solution Keys 180 N 12 Orange Shift P/YR 10 I/YR 150000 PV 0 FV PMT

Present Value What is the PV of receiving $1,000 two years from today if the interest rate is 10%?

Solution Keys 2 N 10 I/YR 1000 FV 0 PMT PV

Annual Payments You want to buy a car that costs $36,000. Your dealer offers you 5 year financing at a 7% interest rate. Find your annual payment.

Solution Keys 36000 PV 5 N 7 I/YR 1 Orange Shift P/YR 0 FV PMT

IRR Suppose you want to buy a car. You are offered two payment options by the dealer 1. Pay today in cash $36,000 2. Make 3 annual payments (first payment is one year from today) of $13,500 What is the IRR?

Solution Keys: -36000 CFi 13500 CFi 13500 CFi 13500 CFi Orange Shift IRR/YR or 3 N 1 Orange Shift P/YR 36000 PV -13500 PMT 0 FV I/YR

What is the present Value of the following set of cash flows, discounted at 10.8% per year? CF=Yr1.$10, Yr2.$22, Yr3$34, Yr. 4$46, Yr5.$58

Solution Keys: N=1 I/YR=10.8 FV=10 PV=? plus N=2 I/YR=10.8 FV=22 PV=? plus N=3 I/YR=10.8 FV=34 PV=? plus N=4 I/YR=10.8 FV=46 PV=? plus N=5 I/YR=10.8 FV=58 PV=? Total sum

Consider again the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons. Suppose interest rates drop and the bond's yield to maturity decreases to 2%. What price is the bond trading for now? What is the effective annual yield on this bond?

Solution Keys: N=10 I/YR=2 PMT=11 FV=1,000 P/YR=2 PV=?

Your cousin is currently 14 years old. she will begin going to college in 4 years. Your aunt and uncle would like to have $105,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3.9% per year, how much money do they need to put into the account today to ensure that they will have $105,000 in 4 years

Solution Keys: N=4 FV=105,000 I/YR=3.9% PV=?

The PV of $230 received in 5 years if the interest rate is 7% Per year is?

Solution Keys: N=5 I/YR=7% FV=230 PV=?

Computing a Loan APR What is the APR on a five year car loan of $24,500 with monthly payments of $500.

Solution Keys: P/Y = 12 PV = $24,500 PMT = -$500 N = 5 x 12 = 60 Then solve for I/Y.

Number of Periods You owe $1,000 in your credit card. Your interest rate is 20%. You plan to make monthly payments of $50 each month. How long until you pay the whole balance?

Solution keys: 1000 PV -50 PMT 20 I/YR 12 Orange Shift P/YR 0 FV N

Assume we are at the first day of 2015. Consider a U.S. government bond with a 6 3/8% coupon that expires in December 2019. The Par or face Value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). On January 1, 2015 the size and timing of cash flows are: The market interest rate for a US government bond of this maturity is now 5% What is the price of the bond?

Solution keys: P/YR=2 N=10 I/Y=5 PMT=31.875=1,000x.06375/2 FV=1,000 PV?- 1,060.17(solve)

The british Gov has a console bond outstanding paying $500 per year forever. assume the current interest rate is 16% per year a. what is the value of the bond immediately after a payment is made? b.what is the value of the bond immediately before a payment is made

a. PV=C/r b.PV=(C/r)+C Where C= Cash flow & r=discount rate(input percentage as decimal)

assume that a bond will make payments every six months as shown on the following timeline a.what is the maturity bond (in years)? b. what is coupon rate(as percent)? periods=40 cash flows=19.82 face value=$1,000

coupon rate=(CPN X # of coupon payments per year)/face value

you are considering two ways of financing a spring break vacation. you could put it on your credit card, at 17% APR, compounded monthly, or borrow the money from your parents, who want an 9% interest payment every 6 months. which is the lower rate?

credit card EAR=((1+(APR/M))^M-1 ((1+(.17/12))^12-1 x100=18.39% Parents loan EAR=(1+r)^M-1 (1.09)^2-1 x100=18.81%

your bank is offering you an account that will pay 22% interest(an effective two year rate) in total for a two year deposit. determine the equivalent discount rate for the following periods: a.6 months b.1 Year c.1 month

equivalent n-period discount rate=(1+r)^n-1 then x 100 to get percentage example 1.(1.22)^(1/4)-1 x100 = answer

if the rate of inflation is 6.2%, what nominal interest rate is necessary for you to earn a 4.1% real interest rate on your investment

nominal rate=real rate x(1+inflation rate) + inflation rate