FIN 3403-CHAPTER 5

Ursula wants to buy a $19,000 used car. She has savings of $2,000 plus an $800 trade-in. She wants her monthly payments to be about $282. Which of the following loans offers monthly payments closest to $282? A) 7.8% APR for 48 monthsB) 7.8% APR for 36 monthsC) 7.8% APR for 60 monthsD) 7.8% APR for 72 months

D) 7.8% APR for 72 monthsExplanation: Calculate N when PV of ordinary annuity = 19k - 2k - 800= 16,200, periodic interest = 7.8/12 %, and monthly payments = 282

A truck costing $111,000 is paid off in monthly installments over four years with 8.10% APR. After three years the owner wishes to sell the truck. What is the closest amount from the following list that he needs to pay on his loan before he can sell the truck? $24,956 $37,434 $31,195 $43,673

$31,195

A homeowner has a $227,000 home with a 20-year mortgage, paid monthly at 6.60% APR. After five years he receives $50,000 as an inheritance. If he pays this $50,000 toward his mortgage along with his regular payment, by approximately how many years will it reduce the amount of time it takes him to pay off his mortgage? 5.5 years 8.6 years 10.2 years 12.8 years

A) The first step is to calculate the monthly payment using a present value (PV) of $227,000 , monthly interest rate of 6.60/12 = 0.55%, and 240 periods,which = $1705.842 ; the second step is to use that monthly payment to calculate the balance at the end of five years, which = $194,594.353 ; next step is to reduce this balance by $50,000 to the new outstanding balance of $144,594.353 ; now calculate the number of months required to pay off this balance,which = 114.45 ; the last step is to calculate the difference between 180 - 114.45 = 65.55 , when divided by 12 gives 5.5 years.

Which of the following best describes the annual percentage rate? Group of answer choices: A. the quoted interest rate which, considered with the compounding period, gives the effective interest rate B. the effective annual rate, after compounding is taken into account C. the discount rate, when compounded more than once a year or less than once a year D. the discount rate, when effective annual rate is divided by the number of times it is compounded in a year

A) the quoted interest rate which, considered with the compounding period, gives the effective interest rate

Which of the following accounts has the highest EAR? Group of answer choices A. one that pays 5.4% every six months B. one that pays 1.0% per month C. one that pays 9.6% per year D. one that pays 2.4% every three months

A. one that pays 5.4​% every six months 1.054^2-1 = 11.09% B. one that pays 1​% per month 1.01^2-1 = 12.68% C. one that pays 2.4​% every three months 1.024^4-1 = 9.95% D. one that pays 9.6​% per year 1.096^1-1 = 9.6% Ans is B

Why, in general, do investment opportunities offer a rate greater than that offered by U.S. Treasury securities for the same horizon? A.Most investment opportunities bear far greater risk than those offered by U.S. Treasury securities.B) The return from U.S. Treasury securities generally attracts less tax than the returns from other investments.C) The opportunity cost of capital for a given horizon is generally based on U.S. Treasury securities with that same horizon.D) U.S. Treasury securities are generally considered to be the best alternative to most investments.

A.Most investment opportunities bear far greater risk than those offered by U.S. Treasury securities

In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in2007? 1.58% 1.61% 1.62% 1.65%

According to fishers effect (1+rn)=(1+rr)(1+ri) Where rn is nominal rate =4.5% Rr is real rate = x R is is inflation = 2.8% (1.045)=(1.028)(1+x) 1+x = 1.0165 So x is 1.65% So correct answer is option D

If the current inflation rate is 2.0%, then the nominal rate necessary for you to earn a(n) 7.3% real interest rate on your investment is closest to ________. Group of answer choices 11.3% 9.4% 13.2% 15.1%

According to the Fisher Effect, ( 1 + Nominal Interest Rate ) = ( 1 + Real Interest Rate) x ( 1 + Inflation Rate ) 1 + Nominal Rate = 1.02 x 1.08073= Nominal Rate = 1.134 - 1 = =(1.02*1.073)-1 =9.4%

A bank offers a loan that will requires you to pay 7% interest compounded monthly. Which of the following is closest to the EAR charged by the bank? 5.78% 8.68% 7.23% 14.46%

C) EAR = {(1 + APR) / m}m - 1; EAR = {(1 + 0.07) / 12}12 - 1; 0.0723 × 100 = 7.23%

Term in years:2 5 10 30 Rate: 2.25% 3.125% 3.5% 4.375% The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. If an investment offers a risk-free cash flow of $100,000 in two years' time, what is the present value (PV) of that cash flow? $76,518 $114,777 $133,906

D) Using FV = $100,000 , find the present value (PV) at 2.25% for 2 yearS The risk free cash flow $100,000 to be received in 2 years is discounted at risk free rate of 2 years 2.25% to get present value of $100,000. The present value of cash flow= $100,000/(1+2.25%)2 The present value of cash flow= $100,000/(1+0.0225)2 The present value of cash flow= $100,000/(1.0225)2 The present value of cash flow= $100,000/1.04550625 The present value of cash flow= $ 95,647.44

Consider the following investment alternatives: Investment,APR,Compounding A,6.0860%,Annual B,5.9320%,Daily C,5.9997%,Quarterly D,5.9936%,Monthly The highest effective rate of return you could earn on any of these investments is closest to ________

EAR (A) = (1 + APR / m)m - 1 = (1 + 0.060860/1)1 - 1 = 6.0860% EAR (B) = (1 + APR / m)m - 1 = (1 + 0.059320 /365)365 - 1 = 6.1110% EAR (C) = (1 + APR / m)m - 1 = (1 + 0.059997/4)4 - 1 = 6.1360% EAR (D) = (1 + APR / m)m - 1 = (1 + 0.059936 /12)12 - 1 = 6.1610% ANSWER c

The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to ________. Group of answer choices: 8.30% 9.13% 9.96% 10.79%

EAR = (1+ (APR/m))^m - 1, where m = no of compounding per year EAR = (1+ (APR/12))^12 - 1 EAR = (1 + (0.08/12))^12 - 1 = 1.083 - 1 = 0.083 = 8.3%

An animator needs a laptop for audio/video editing, and notices that he can pay $2600 for a Dell XPS laptop, or lease from the manufacturer for monthly payments of $75 each for four years. The designer can borrow at an interest rate of 14% APR compounded monthly. What is the cost of leasing the laptop over buying it outright? Group of answer choices A. Leasing costs $116 more than buying. B. Leasing costs $174 more than buying. C. Leasing costs $145 more than buying. D. Leasing costs $289 more than buying.

Find the present value of the monthly payments for four years. PV of annuity = P*[(1-(1+r)^(-n)) / r] P - Periodic payment = 75 r - rate per period = 0.14/12 n - number of periods = 4*12 = 48 PV of annuity = 75*((1-(1+(0.14/12))^(-48)) / (0.14/12)) = $2744.59 Cost of leasing over buying = 2744.59 - 2600 = $144.59 c. C. Leasing costs $145 more than buying.

What is the effective annual rate (EAR)? Group of answer choices: A.It is the interest rate that would earn the same interest with annual compounding. B.It is the ratio of the number of the annual percentage rate to the number of compounding periods per year. C.It is the interest rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction). D.It refers to the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year.

It is the interest rate that would earn the same interest with annual compounding.

Which of the following would be LEAST likely to lower the interest rate that a bank offers a borrower? Group of answer choices The number of borrowers seeking funds is low. The expected inflation rate is expected to be low. The borrower is judged to have a low degree of risk. The loan will be for a long period of time.

The loan will be for a long period of time.

Five years ago you took out a 30-year mortgage with an APR of 6.5% for $200,000. If you were to refinance the mortgage today for 20 years at an APR of 4.25%, how much would your monthly payment change by? The monthly payment will increase by $104.79. The monthly payment will decrease by $104.79 The monthly payment will increase by $343.12. The monthly payment will decrease by $343.12.

The monthly payment will decrease by $104.79

A $52,000 loan is taken out on a boat with the terms 3% APR for 36 months. How much are the monthly payments on this loan?

This question requires application of PV of annuity concept, according to which PV =p * (1-(1-R)^-N)/R r = 3%/12 = 0.25% (monthly), n = 36, PV = 52,000 52000 = P * 34.386465 P = $1,512.22

A homeowner has five years remaining of monthly payments of $1400 before she will pay off her house. If the interest rate is 6% APR, what is the remaining balance on her loan?

USE EXCEL =PV(0.06/12,60,1400,0,0)= $72,416

What is the present value (PV) of an investment that pays $100,000 every year for four years if the interest rate is 5% APR, compounded quarterly?

effective rate of interest = (1+(r/n))^n - 1 where r = APR = 5% n = compounding periods = 4 Effective annual rate = (1 + (5%/4))^4 - 1 = 5.0945% present value of annuity = P*[1 - (1+r)^-n / r ] where P = annual Payments = 100,000 r = rate of interest = 5.0945% n = number of periods = 4 Present value = 100,000*[(1 - (1+5.0945%)^-4 / 5.0945% ] = $353,818 Option B is correct

A pottery factory purchases a continuous belt conveyor kiln for $68,000. A 6.3% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $765.22, over what term is this loan being paid?

where A = payment Amount per period P = initial Principal (loan amount) r = interest rate per period n = total number of payments or periods A = $ 765.22 P = $68,000 r = 6.3%, monthly rate = 6.3%/12 = 0.53% n=??? 765.22 = 68,000 * 0.53%(1+0.53%)^n/(1+0.53%)^n-1 n = 120 or 10 years