FIN 311 Chapter 6: Discounted Cash Flow Valuation

How frequently does continuous compounding occur? a) 100 times a year b) 1,000,000 times a year c) Every instant d) 1,000 times a year

c) Every instant

You want to buy a new sports car from Muscle Motors for $64,500. The contract is in the form of a 60-month annuity due at an APR of 5.4 percent. What will your monthly payment be?

$1,223.54 We need to use the PVA due equation, that is: PVAdue = (1 + r)PVA Using this equation: PVAdue = $64,500 = [1 + (.054/12)] × C[{1 − 1/[1 + (.054/12)]^60}/(.054/12)] $64,211.05 = C{1 − [1/(1 + .054/12)^60]}/(.054/12) C = $1,223.54 Notice, to find the payment for the PVA due we compound the payment for an ordinary annuity forward one period. How to do it on the financial calculator: 2nd BGN 2nd SET PV = -$64,500 I/Y = 5.4/12 N = 60 CPT PMT = $1,223.54

The present value of the following cash flow stream is $8,200 when discounted at 9 percent annually. What is the value of the missing cash flow? Year------Cash Flow 1 ----------- $2,100 2 ---------- __________ 3 ---------- $2,740 4 ---------- $3,270

$2,187.36 We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are: PV of Year 1 CF: $2,100/1.09 = $1,926.61 PV of Year 3 CF: $2,740/1.09^3 = $2,115.78 PV of Year 4 CF: $3,270/1.09^4 = $2,316.55 So, the PV of the missing CF is: PV of missing cash flow = $8,200 − 1,926.61 − 2,115.78 − 2,316.55 PV of missing cash flow = $1,841.06 The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is: Missing cash flow = $1,841.06(1.09^2) Missing cash flow = $2,187.36 How to do it on the financial calculator: CF0 = $0 C01 = $2,100 F01 = 1 C02 = $0 F02 = 1 C03 = $2,740 F03 = 1 C04 = $3,270 F04 = 1 I = 9 NPV CPT PV of missing CF = $8,200 − 6,358.94 = $1,841.06 Value of missing CF: PV = -$1,841.06 I/Y = 9 N = 2 CPT FV

When the U.S. government wants to borrow money for the long-term (more than one year) it issues: - Treasury bills - Treasury bonds - Treasury stocks - Treasury notes

- Treasury bonds - Treasury notes Reason(s) why it's not the other options: - Treasury bills are short term-one year or less - The U.S. Treasury does not issue stock

You're prepared to make monthly payments of $225, beginning at the end of this month, into an account that pays an APR of 6.5 percent compounded monthly. How many payments will you have made when your account balance reaches $15,000?

57.07 Here we are given the FVA, the interest rate, and the amount of the annuity. We need to solve for the number of payments. Using the FVA equation: FVA = $15,000 = $225[{[1 + (.065/12)]^t − 1}/(.065/12)] Solving for t, we get: 1.00542^t = 1 + ($15,000/$225)(.065/12) t = ln 1.36111/ln 1.00542 t = 57.07 payments How to do it on the financial calculator: PMT = -$225 FV = $15,000 I/Y = 6.5/12 CPT N

Match the type of rate with its definition APR EAR The interest rate stated as though it were compounded once per year The interest rate per period multiplied by the number of periods in the year

APR <------> The interest rate per period multiplied by the number of periods in the year EAR <------> The interest rate stated as though it were compounded once per year

You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you an APR of 4.7 percent for a 60-month loan to buy the car. a) What will your monthly payment be? b) What is the effective annual rate on this loan?

a) $1,583.03 b) 4.8% We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation: PVA = C({1 − [1/(1 + r)^t]}/r) $84,500 = $C[1 − {1/[1 + (.047/12)]^60}/(.047/12)] Solving for the payment, we get: C = $84,500/53.3786C = $1,583.03 To find the EAR, we use the EAR equation: EAR = [1 + (APR/m)]^m − 1 EAR = [1 + (.047/12)]^12 − 1 EAR = .0480, or 4.80% How to do it on the financial calculator: a) PV = -$84,500 I/Y = 4.7/12 N = 60 CPT PMT b) NOM = 4.7 C/Y = 12 CPT EFF

You want to be a millionaire when you retire in 40 years. a) How much do you have to save each month if you can earn an APR of 10.2 percent? b) How much do you have to save each month if you wait 10 years before you begin your deposits? c) How much do you have to save each month if you wait 20 years before you begin your deposits?

a) $148.77 b) $423.87 c) $1,283.10 Starting today: FVA = C[{[1 + (.102/12)]^480 − 1}/(.102/12)] C = $1,000,000/6,721.6946 C = $148.77 Starting in 10 years: FVA = C[{[1 + (.102/12)]^360 − 1}/(.102/12)] C = $1,000,000/2,359.2388 C = $423.87 Starting in 20 years: FVA = C[{[1 + (.102/12)]^240 − 1}/(.102/12)] C = $1,000,000/779.3638 C = $1,283.10 How to do it on the financial calculator: a) FV = -$1,000,000 I/Y = 10.2/12 N = 480 CPT PMT b) FV = -$1,000,000 I/Y = 10.2/12 N = 360 CPT PMT c) FV = -$1,000,000 I/Y = 10.2/12 N = 240 CPT PMT

You plan to deposit $4,900 at the end of each of the next 20 years into an account paying 10.3 percent interest. a) How much money will you have in the account in 20 years? b) How much will you have if you make deposits for 40 years?

a) $290,390.14 b) $2,353,356.38 Here we need to find the FVA. The equation to find the FVA is: FVA = C{[(1 + r)^t −1]/r} a) FVA for 20 years = $4,900[(1.103^20 −1)/.103] = $290,390.14 b) FVA for 40 years = $4,900[(1.103^40 −1)/.103] = $2,353,356.38 How to do it on the financial calculator: a) PMT = -$4,900 I/Y = 10.3 N = 20 CPT FV b) PMT = -$4,900 I/Y = 10.3 N = 40 CPT FV

The future value factor for a(n) ______ is found by taking the future value factor and subtracting one, then dividing this number by the interest rate.

annuity

The present value of a(n) ______ of C dollars per period for t periods when the rate of return or interest rate, r, is given by: C × (1 − [1/(1 + r)t]r/)

annuity

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _____ of each period. a) beginning b) end c) middle

b) end

An annuity due is a series of payments that are made ____. a) 1 year in the past b) 1 year hence c) at the beginning of each period d) any time in the future

c) at the beginning of each period

Most investments involve ______ cash flows. a) single b) no c) multiple d) lump sum

c) multiple

Because of __________ and _________, interest rates are often quoted in many different ways. a) mathematics; evolution b) religion; randomness c) tradition; legislation

c) tradition; legislation

In terms of time to maturity, U.S. Treasury notes and bonds have initial maturities ranging from ___ years. a) 10 to 30 b) 5 to 20 c) 5 to 25 d) 2 to 30

d) 2 to 30

Which of the following is a perpetuity? a) An undulating stream of cash flows forever b) A growing stream of cash flows for a fixed period c) A constant stream of cash flows for a fixed period d) A constant stream of cash flows forever

d) A constant stream of cash flows forever

A perpetuity is a constant stream of cash flows for a(n) ______ period of time. a) infinite b) finite c) random d) undetermined

a) infinite

Which of the following are annuities? - Installment loan payments - Monthly grocery bill - Monthly rent payments in a lease - Tips to a waiter

- Installment loan payments - Monthly rent payments in a lease Reason(s) why it's not the other options: This is not a level cash flow

The formula for the annuity present value factor for a 30-year annuity with an interest rate of 10 percent per year is ______. a) [1-(1/1.10^30)]/.10 b) [1-(1/1.20^30)]/.10 c) [1-(1.1/1.10^30)]/.10 d) [1-(1/1.10^30)]/.20

a) [1-(1/1.10^30)]/.10

Which formula shows the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10 percent per year? a) $1,100{[1 − (1/(1.10)^3)]/0.20} b) $100{[1 − (1/(1.10)^3)]/1.20} c) $1,000{[1 − (1/(1.10)^3)]/0.10} d) $100{[1 − (1/(1.10)^3)]/0.10}

d) $100{[1 − (1/(1.10)^3)]/0.10}

Which of the following are real-world examples of annuities? - Pensions - Common stock dividends - Mortgages

- Pensions - Mortgages Reason(s) why it's not the other options: - Common stock dividends are not annuities - they are not required to be paid and when they are paid the amount can not be known in advance for certain.

George Jefferson established a trust fund that will provide $170,500 per year in scholarships. The trust fund earns an annual return of 2.1 percent. How much money did Mr. Jefferson contribute to the fund assuming that only income is distributed? a) $7,104,166.67 b) $8,119,047.62 c) $9,278,911.56 d) $6,765,873.02 e) $7,494,505.49

b) $8,119,047.62 PV = $170,500/.021 = $8,119,047.62

Which one of the following statements concerning interest rates is correct? a) Savers would prefer annual compounding over monthly compounding given the same annual percentage rate. b) The effective annual rate decreases as the number of compounding periods per year increases. c) The effective annual rate equals the annual percentage rate when interest is compounded annually. d) Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate. e) For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate.

c) the effective annual rate equals the annual percentage rate when interest is compounded annually

The U.S. government borrows money by issuing: - Treasury pass-through certificates - Treasury notes - Treasury bonds - Treasury bills

- Treasury notes - Treasury bonds - Treasury bills

The appropriate discount rate for the following cash flows is 9.32 percent per year. Year/Cash Flow: 1/$2,480 2/$0 3/$3,920 4/$2,170 What is the present value of the cash flows?

$6,789.39 Here the cash flows are annual and the given interest rate is annual, so we can use the interest rate given. We find the PV of each cash flow and add them together. PV = $2,480/1.0932 + $3,920/1.0932^3 + $2,170/1.0932^4 = $6,788.39 How to do it on the financial calculator: CF0 = $0 C01 = $2,480 F01 = 1 C02 = $0 F02 = 1 C03 = $3,920 F03 = 1 C04 = $2,170 F04 = 1 I = 9.32% NPV CPT

Which of the following should be valued using a perpetuity formula? - A consol (bond that pays interest only and does not mature) - Cash flows from a product whose sales are expected to remain constant forever - An amortized loan with a set amount over a period of time - Preferred stock

- A consol (bond that pays interest only and does not mature) - Cash flows from a product whose sales are expected to remain constant forever - Preferred stock Reason(s) why it's not the other options: An amortized loan has a maturity date, and therefore is not a perpetuity.

Given a discount rate of 4.6 percent per year, what is the value at Date t = 7 of a perpetual stream of $7,300 payments with the first payment at Date t = 15?

$115,835.92 To find the value of the perpetuity at t = 7, we first need to use the PV of a perpetuity equation. Using this equation, we find: PV = $7,300/.046 PV = $158,695.65 Remember that the PV of perpetuity (and annuity) equations give the PV one period before the first payment, so this is the value of the perpetuity at t = 14. To find the value at t = 7, we find the PV of this lump sum as: PV = $158,695.65/1.0467 PV = $115,835.92 How to do it on the financial calculator: PV@ Time = 14: $7,300/.046 = $158,695.65 FV = -$158,695.65 I/Y = 4.6 N = 7 CPT PV = $115,835.92

When calculating the future value of multiple cash flows using a spreadsheet, you must: a) Calculate the future value of each cash flow then add the compounded values together b) Use the time value of money tables to calculate the future value of each cash flow c) Calculate the present value of each cash flow then add the discounted values together

a) Calculate the future value of each cash flow then add the compounded values together Reason(s) why it's not the other options: b) Spreadsheets have time value of money functions, so the tables are unnecessary

An effective annual rate of 7.12 percent is equal to 7 percent compounded ______. a) daily b) quarterly c) semiannually d) continuously

c) semiannually For semiannual compounding, EAR = ((1+0.07/2)^2) - 1 = 7.12% Reason(s) why it's not the other options: a) For daily compounding, EAR = ((1+0.07/365)^365) - 1 = 7.25% b) For quarterly compounding, EAR = ((1 +0.07/4)^4) - 1 = 7.19% c) For continuous compounding, EAR = (e^0.07) - 1 = 7.251%

You want to retire exactly 40 years from today with $2,060,000 in your retirement account. If you think you can earn an interest rate of 10.51 percent compounded monthly, how much must you deposit each month to fund your retirement? a) $276.27 b) $337.50 c) $4,291.67 d) $278.69 e) $297.27

d) $278.69 $2,060,000 = C[((1 + .1051/12)480 − 1)/(.1051/12)] C = $278.69 How to do it on the financial calculator: FV = -$2,060,000 I/Y = 10.51/12 N = 40(12) CPT PMT = $278.69

One method of calculating future values for multiple cash flows is to compound the accumulated balance forward _____ at a time. a) two years b) half a year c) three years d) one year

d) one year

You are in talks to settle a potential lawsuit. The defendant has offered to make annual payments of $27,000, $31,000, $64,000, and $96,000 to you each year over the next four years, respectively. All payments will be made at the end of the year. If the appropriate interest rate is 4.9 percent, what is the value of the settlement offer today? a) $218,000.00 b) $197,878.37 c) $203,317.62 d) $167,675.77 e) $188,635.24

e) $188,635.24 PV = $27,000/1.049 + $31,000/1.0492 + $64,000/1.0493 + $96,000/1.0494 = $188,635.24 How to do it on the financial calculator: CF0 = $0 C01 = $27,000 F01 = 1 C02 = $31,000 F02 = 1 C03 = $64,000 F03 = 1 C04 = $96,000 F04 = 1 I = 4.9 NPV CPT = $188,635.24

You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while Annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities? a) These annuities have equal present values but unequal future values. b) These two annuities have both equal present and equal future values. c) Annuity B is an annuity due. d) Annuity A has a smaller future value than Annuity B. e) Annuity B has a smaller present value than Annuity A.

e) Annuity B has a smaller present value than Annuity A

What is the value today of $5,100 per year, at a discount rate of 7.9 percent, if the first payment is received 6 years from today and the last payment is received 20 years from today?

$30,030.78 We want to find the value of the cash flows today, so we will find the PV of the annuity, and then bring the lump sum PV back to today. The annuity has 15 payments, so the PV of the annuity is: PVA = $5,100{[1 − (1/1.079^15)]/.079} PVA = $43,921.16 Since this is an ordinary annuity equation, this is the PV one period before the first payment, so this is the PV at t = 5. To find the value today, we find the PV of this lump sum. The value today is: PV = $43,921.16/1.079^5 PV = $30,030.78 How to do it on the financial calculator: PMT = -$5,100 I/Y = 7.9 N = 15 CPT PV = $43,921.16 FV = -$43,921.16 I/Y = 7.9 N = 5 CPT PV

Investment X offers to pay you $5,300 per year for eight years, whereas Investment Y offers to pay you $7,300 per year for five years. a) Calculate the present value for Investment X and Y if the discount rate is 5 percent. b) Calculate the present value for Investment X and Y if the discount rate is 15 percent.

a) PV of X at 5% = $34,255.03 a) PV of Y at 5% = $31,605.18 b) PV of X at 15% = $23,782.80 b) PV of Y at 15% = $24,470.73 To find the PVA, we use the equation: PVA = C({1 − [1/(1 + r)^t]}/r) At a 5 percent interest rate: X@5%: PVA = $5,300{[1 − (1/1.05)^8]/.05} = $34,255.03 Y@5%: PVA = $7,300{[1 − (1/1.05)^5]/.05} = $31,605.18 And at a 15 percent interest rate: X@15%: PVA = $5,300{[1 − (1/1.15)^8]/.15} = $23,782.80 Y@15%: PVA = $7,300{[1 − (1/1.15)^5]/.15} = $24,470.73 Notice that the cash flow of X has a greater PV at a 5 percent interest rate, but a lower PV at a 15 percent interest rate. The reason is that X has greater total cash flows. At a lower interest rate, the total cash flow is more important since the cost of waiting (the interest rate) is not as great. At a higher interest rate, Y is more valuable since it has larger cash flows. At the higher interest rate, these larger cash flows early are more important since the cost of waiting (the interest rate) is so much greater. How to do it on the financial calculator: a) PMT = -$5,300 I/Y = 5 N = 8 CPT PV a) PMT = -$7,300 I/Y = 5 N = 5 CPT PV b) PMT = -$5,300 I/Y = 15 N = 8 CPT PV b) PMT = -$7,300 I/Y = 15 N = 5 CPT PV

The formula for the present value interest factor for annuities is: Annuity present value factor = {1-[1/(1+r)^t]}/r. a) True b) False

a) True Reason(s) why it's not the other options: This is the formula for the PVIF

A growing annuity has a(n) ______. a) finite number of growing cash flows b) infinite number of constant cash flows c) infinite number of growing cash flows d) finite number of level cash flows

a) finite number of growing cash flows

Interest paid twice a year is known as ______ compounding. a) semiannual b) biannual c) weekly d) monthly

a) semiannual

The ______ percentage rate is the interest rate charged per period multiplied by the number of periods in a year.

annual

A 15-year annuity pays $1,750 per month, and payments are made at the end of each month. If the APR is 9 percent compounded monthly for the first seven years, and APR of 6 percent compounded monthly thereafter, what is the value of the annuity today?

$179,859.81 This question is asking for the present value of an annuity, but the interest rate changes during the life of the annuity. We need to find the present value of the cash flows for the last eight years first. The PV of these cash flows is: PVA2 = $1,750{1 − 1/[1 + (.06/12)]^96}/(.06/12)] PVA2 = $133,166.63 Note that this is the PV of this annuity exactly seven years from today. Now we can discount this lump sum to today. The value of this cash flow today is: PV = $133,166.63/[1 + (.09/12)]^84 PV = $71,090.38 Now we need to find the PV of the annuity for the first seven years. The value of these cash flows today is: PVA1 = $1,750[{1 − 1/[1 + (.09/12)]^84}/(.09/12)] PVA1 = $108,769.44 The value of the cash flows today is the sum of these two cash flows, so: PV = $71,090.38 + 108,769.44 PV = $179,859.81 How to do it on the financial calculator: PMT = -$1,750 I/Y = 6/12 N = 96 CPT PV = $133,166.63 FV = -$133,166.63 I/Y = 9/12 N = 84 CPT PV = $71,090.38 PMT = -$1,750 I/Y = 9/12 N = 84 CPT PV = $108,769.44 $71,090.38 + $108,769.44 = $179,859.81

You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: (a) The present value of two years' back pay. The plaintiff's annual salary for the last two years would have been $43,000 and $46,000, respectively. (b) The present value of five years' future salary. You assume the salary will be $51,000 per year. (c) $150,000 for pain and suffering. (d) $20,000 for court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is an EAR of 5.9 percent, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate? a) Higher interest rate b) Lower interest rate

$485,167.86 b) Lower interest rate Here we have cash flows that would have occurred in the past and cash flows that will occur in the future. We need to bring both cash flows to today. Before we calculate the value of the cash flows today, we must adjust the interest rate so we have the effective monthly interest rate. Finding the APR with monthly compounding and dividing by 12 will give us the effective monthly rate. The APR with monthly compounding is: APR = 12[(1.059)^(1/12) − 1] APR = .0575, or 5.75% To find the value today of the back pay from two years ago, we will find the FV of the annuity, and then find the FV of the lump sum. Doing so gives us: FVA = ($43,000/12)[{[1 + (.0575/12)]^12 − 1}/(.0575/12)] FVA = $44,150.76 FV = $44,150.76(1.059) FV = $46,755.65 Notice we found the FV of the annuity with the effective monthly rate, and then found the FV of the lump sum with the EAR. Alternatively, we could have found the FV of the lump sum with the effective monthly rate as long as we used 12 periods. The answer would be the same either way. Now, we need to find the value today of last year's back pay: FVA = ($46,000/12)[{[1 + (.0575/12)]^12 − 1}/(.0575/12)] FVA = $47,231.04 Next, we find the value today of the five years' future salary: PVA = ($51,000/12){[(1 − {1/[1 + (.0575/12)]^(12(5))})/(.0575/12)]} PVA = $221,181.17 The value today of the jury award is the sum of salaries, plus the compensation for pain and suffering, and court costs. The award should be for the amount of: Award = $46,755.65 + 47,231.04 + 221,181.17 + 150,000 + 20,000 Award = $485,167.86 As the plaintiff, you would prefer a lower interest rate. In this problem, we are calculating both the PV and FV of annuities. A lower interest rate will decrease the FVA, but increase the PVA. So, by a lower interest rate, we are lowering the value of the back pay. But, we are also increasing the PV of the future salary. Since the future salary is larger and has a longer time, this is the more important cash flow to the plaintiff. How to do it on the financial calculator: EFF = 5.9 C/Y = 12 CPT NOM = 5.75% PMT = -$43,000/12 I/Y = 5.75/12 N = 12 CPT FV = $44,150.76 PV = -$44,150.76 I/Y = 5.9 N = 1 CPT FV = $46,7555.65 PMT = -$46,000/12 I/Y = 5.75/12 N = 12 CPT FV = $47,231.04 PMT = -$51,000/12 I/Y = 5.75/12 N = 60 CPT PV = $221,181.17 Award = $46,755.65 + 47,231.04 + 221,181.17 + 150,000 + 20,000 = $485,167.86

Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $15,000 balance from your current credit card, which charges an annual rate of 18.6 percent, to a new credit card charging a rate of 9.2 percent. a) How much faster could you pay the loan off by making your planned monthly payments of $275 with the new card? b) What if there was a fee of 2 percent charged on any balances transferred?

a) 50.49 b) 48.59 We will calculate the number of periods necessary to repay the balance with no fee first. We need to use the PVA equation and solve for the number of payments. Without fee and annual rate = 18.60%: PVA = $15,000 = $275{[1 − (1/1.0155^t)]/.0155} where .0155 = .186/12 Solving for t, we get: 1/1.0155^t = 1 − ($15,000/$275)(.0155) 1/1.0155^t = .155 t = ln(1/.155)/ln 1.0155 t = 121.40 months Without fee and annual rate = 9.2%: PVA = $15,000 = $275{[1 − (1/1.00767^t)]/.00767} where .00767 = .092/12 Solving for t, we get: 1/1.00767^t = 1 − ($15,000/$275)(.00767) 1/1.00767^t = .582 t = ln(1/.582)/ln 1.00767 t = 70.91 months So, you will pay off your new card: Months quicker to pay off card = 121.40 − 70.91 Months quicker to pay off card = 50.49 months Note that we do not need to calculate the time necessary to repay your current credit card with a fee since no fee will be incurred. It will still take 121.40 months to pay off your current card. The time to repay the new card with a transfer fee is: With fee and annual rate = 9.2%: PVA = $15,300 = $275{[1 − (1/1.00767)^t]/.00767} where .00767 = .092/12 Solving for t, we get: 1/1.00767^t = 1 − ($15,300/$275)(.00767) 1/1.00767^t = .573 t = ln(1/.573)/ln 1.00767 t = 72.81 months So, you will pay off your new card: Months quicker to pay off card = 121.40 − 72.81 Months quicker to pay off card = 48.59 months How to do it on the financial calculator: a) PMT = -$275 PV = $15,000 I/Y = 18.6/12 CPT N = 121.40 PMT = -$275 PV = $15,000 I/Y = 9.2/12 N = 70.91 Months quicker to pay off card = 121.40 − 70.91 = 50.49 months b) PMT = -$275 PV = $15,300 I/Y = 9.2/12 CPT N = 72.81 Months quicker to pay off card = 121.40 - 72.81 = 48.59 months

You want to buy a house and will need to borrow $265,000. The interest rate on your loan is 6.01 percent compounded monthly and the loan is for 20 years. What are your monthly mortgage payments? a) $1,836.74 b) $1,900.07 c) $1,890.60 d) $1,995.07 e) $1,926.89

b) $1,900.07 $265,000 = C{1 − 1/[1 + (.0601/12)]240}/(.0601/12) C = $1,900.07 How to do it on the financial calculator: PV = -$265,000 I/Y = 6.01/12 N = 20(12) CPT PMT = $1,900.07

Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this money to his favorite charity by making three equal donations at the end of the next 3 years. How much will Ralph give to the charity each year? a) $397.66 b) $402.11 c) $412.98 d) $405.63

b) $402.11 Reason(s) why it's not the other options: Calculate the payment using the PV of an annuity at 10 percent for 3 years. $1,000/[(1-1/1.10^3)/0.10] = $402.11

True or false: There is only one way to quote interest rates. a) True b) False

b) False

Given the same APR, more frequent compounding results in _____. a) rounder EARs b) lower EARs c) higher EARs

c) higher EARs