FIN 325 - Quiz 2

When your father was born 44 years ago, his grandparents deposited $400 in an account for him. Today, that account is worth $40,000. What was the annual rate of return on this account?

11.03% We use the formula:A=P(1+r/100)^nwhereA=future valueP=present valuer=rate of interestn=time period. 40000=400*(1+r/100)^44 (40000/400)^(1/44)=(1+r/100) (1+r/100)=1.1103 r=1.1103-1 =11.03%(Approx).

Assume the total cost of a college education will be $245,000 when your child enters college in 15 years. You presently have $108,000 to invest for this purpose. What annually compounded rate of interest must you earn to cover the cost of your child's college education?

5.61% The correct answer is C that is 5.61%. As per the given question, PV=108000 FV=245000 n=15 by solving we get i=5.61% .

Maxxie purchased a tract of land for $30,000. Today, the same land is worth $44,900. How many years have passed if the price of the land has increased at an annual rate of 5.9 percent?

7.03 years =NPER(5.9%,,-30000,44900)

Assume you intend to retire 47 years from today. Your current salary is $80,000 per year, and you expect to earn salary increases of 3.25 percent each year. What annual salary do you expect to earn 47 years from today?

Current Salary = $80,000 Growth = 3.25% every year for 47 Years A = p(1+r/n)^nt A = Final Amount P = Intial Salary r = Growth rate n = number of times Growth applied per time period t = time period A = 80000(1+0.0325/1)^1*47 A = 80000(1.0325)^47 A= 80000*4.496068 A = 359685.44 Therefore Option 1 Need to selected

The most common type of medium-term, amortized business loans has which one of these characteristics over its life?

Equal principal payments Amortized loans will have mostly unequal principal payments but with fixed periodic payments.

Madelyn is calculating the present value of a bonus she will receive next year. The process she is using is called:

discounting

What is the present value of $45,000 to be received 50 years from today if the discount rate is 8 percent, compounded annually?

$959.46 $959.46- PV => FV/(1 + Discount Rate^Time) = $959.46

A perpetuity is defined as:

unending equal payments paid at equal time intervals

Claire's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much is the collection expected to be worth in 2025?

$14,077.16 We use the formula:A=P(1+r/100)^nwhereA=future valueP=present valuer=rate of interestn=time period. A=50*(1.076)^77 =50*281.543103 =14077.16(Approx).

Thomas invests $119 in an account that pays 5 percent simple interest. How much money will Thomas have at the end of 5 years?

$148.75 Calculate the amount at the end of 5th year: Principal = $119 Rate = 5% Time = 5 years. Formula for interest = (Principle x Time x Rate) / 100 Interest = (119 x 5x 5) / 100 = $29.75 Total Amount = $119 + $29.75 = $148.75

On your tenth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

Age 31 (756/300) = (1.045)^n n = log(1.045)(756/300) = 20.9978 approx 21 year's So the person is 31 years old today

Two annuities have equal present values and an applicable discount rate of 7.25 percent. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?

$2,681.25 Explanation: PaymentEnd = $2,500(1.0725)PaymentEnd = $2,681.25Difficulty: 2 MediumTopic: AnnuitiesLearning Objective: 06-02 Explain how loan payments are calculated and how to find the interest rate on a loan.Bloom's: AnalyzeAACSB: Analytical ThinkingAccessibility:

Assuming an interest rate of 6.2% What is the value of the following cash flows 4 years from today? Year / Cash Flow 1 / $3,200 2 / $4,200 3 / $6,085 4 / $8,215

$23,247.08

Assume you borrow $30,000 at an interest rate of 5.35 percent. The terms stipulate that the principal is due in full in 5 years and interest is to be paid annually at the end of each year. How much total interest will you pay on this loan assuming you pay as agreed?

$8,025

You will receive $4,000 at graduation 3 years from now. You plan on investing this money at 5 percent annually compounded interest until you have accumulated $50,000. How many years from today will it be when this occurs?

54.77 years

Which one of the following statements related to annuities and perpetuities is correct?

A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal.

This morning, Clayton deposited $2,500 into an account that pays 5 percent interest, compounded annually. Also this morning, Jayda deposited $2,500 at 5 percent interest, compounded annually. Clayton will withdraw his interest earnings and spend it as soon as possible. Jayda will reinvest her interest earnings into her account. Given this information, which one of the following statements is true?

Jayda will earn more interest in year 2 than Clayton will earn

Which one of the following statements correctly defines a time value of money relationship?

Time and present value are inversely related, all else held constant.

Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:

could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest.

Jenny Enterprises has just entered a lease agreement for a new manufacturing facility. Under the terms of the agreement, the company agreed to pay rent of $18,500 per month for the next 10 years with the first payment due today. If the APR is 7.92 percent compounded monthly, what is the value of the payments today?

$1,540,222.14

You need $25,000 today and have decided to take out a loan at 7 percent interest for five years. Which one of the following loans would be the least expensive for you? Assume all loans require monthly payments and that interest is compounded on a monthly basis.

Amortized loan with equal principal payments Difficulty: 1 EasyTopic: Types of loansLearning Objective: 06-03 Describe how loans are amortized or paid off.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility:

You have a savings account valued at $1,500 today that earns an annual interest rate of 8.7 percent. How much more would this account be worth if you wait to spend the entire balance in 25 years rather than in 20 years? (Assume annual compounding.)

Answer is $4,117.64 If amount is spend in 25 years: Initial balance = $1,500Interest rate = 8.70%Period = 25 years Accumulated Sum = Initial balance * (1 + Interest rate)^PeriodAccumulated Sum = $1,500 * 1.087^25Accumulated Sum = $12,073.41 If amount is spend in 20 years: Initial balance = $1,500Interest rate = 8.70%Period = 20 years Accumulated Sum = Initial balance * (1 + Interest rate)^PeriodAccumulated Sum = $1,500 * 1.087^20Accumulated Sum = $7,955.77 Additional amount spent = $12,073.41 - $7,955.77Additional amount spent = $4,117.64

According to the Rule of 72, you can do which one of the following?

Approximately double your money in 11 years at 6.55% interest

An ordinary annuity is best defined as:

Equal payments paid at the end of regular intervals over a stated time period. A perpetuity composed of 100 months payments is worth more than an annuity of 100 monthly payments given equals discount rates

When you retire 45 years from now, you want to have $1.25 million saved. You think you can earn an average of 7.6 percent, compounded annually, on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today to fund this goal. How much more will you have to deposit if you wait for five years before making the deposit?

$20,468.85 > ConceptPresent Value = Future Value / ( 1 + r )n > Calculation [ A ] If the lumpsum is deposited now. Then it will remain deposited for 45 years. Present Value = 1250000 / ( 1.076 )45 = 1250000 / 27.0117181736 = 46276.21 [ B ] If the lumpsum is deposited after 5 years. Then it will remain deposited for 40 years. Present Value = 1250000 / ( 1.076 )40 = 1250000 / 18.7279763914 = $ 66745.07 > Answer Extra payment if delay in deposit for 5 years = [ B ] - [ A ] = 66745.07 - 46276.21 = $ 20468.85 Answer

You estimate that you will owe $28,200 in student loans by the time you graduate. If you want to have this debt paid in full within 10 years, how much must you pay each month if the interest rate is 5.4 percent per year compounded monthly?

$304.65 Amount of debt owned at time of graduation (PV)=28200 Number of years to pay debt = 10 Total months (n)=10*12 = 120 Interest rate is 5.4% compounded monthly Periodic or monthly rate = APR/Number of compounding in year =5.4%/12 =0.0045 Amount to be paid each month will be calculated using Annuity formula. Annuity or monthly payment formula = PV* i *((1+i)^n)/((1+i)^n-1) =28200*0.0045*((1+0.0045)^120)/(((1+0.0045)^120)-1) =304.6486666 So we must pay $304.65 each month to pay off the debt.

Jonathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years?

$33,588

What is the future value of $8,500 invested at the end of each year for 40 years, at 10.8 percent interest compounded annually?

$46,891,062.12 Explanation: FVA = $8,500[(1.10840 − 1)/.108]FVA = $4,681,062.12Difficulty: 2 MediumTopic: Future value - annuityLearning Objective: 06-01 Determine the future and present value of investments with multiple cash flows.Bloom's: AnalyzeAACSB: Analytical ThinkingAccessibility:

Gerritt wants to buy a car that costs $29,750. The interest rate on his loan is 5.57 percent compounded monthly and the loan is for 6 years. What are his monthly payments?

$487.03

Your cousin deposited $2,500 today at 6.5 percent interest for 15 years. However, you can only earn 6.25 percent interest. How much more money must you deposit today than your cousin invested if you are to have the same amount saved at the end of the 15 years? (Assume annual compounding on both accounts.)

$89.70 P1 = Amount saved by your brother = $2,500 P2 = Amount saved by you r1 = interest rate = 6.5% n = 15 years r2 = interest rate = 6.25% At the end of 15 years both of you should end up with same balance P1 * (1+r1)^n = P2 * (1+r2)^n $2,500 * (1+6.5%)^15 = P2 * (1+6.25%)^15 $2,500 * 2.57184101 = P2 * 2.48275623 P2 = $2,589.70351 Amount required to deposit today by you is $2,589.70 Difference in amount = $2,589.70 - $2,500 = $89.70 Therefore, increase in amount required to save by you is $89.70

You are preparing to make monthly payments of $100, beginning at the end of this month, into an account that pays 5 percent interest compounded monthly. How many payments will you have made when your account balance reaches $10,000?

83.77 Explanation: FVA = $10,000 = $100({[1 + (.05/12)]t − 1}/(.05/12))t = 83.77 paymentsDifficulty: 2 MediumTopic: Time value of moneyLearning Objective: 06-01 Determine the future and present value of investments with multiple cash flows.Bloom's: AnalyzeAACSB: Analytical ThinkingAccessibility:

Miles invested $5,000 ten years ago and expected to have $10,000 today. He has neither added nor withdrawn any money since his initial investment. All interest was reinvested and compounded annually. As it turns out, he only has $8,400 in his account today. Which one of the following statements must be true?

He earned a lower interest rate than he expected.

As the beneficiary of a life insurance policy, you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. If you can earn 6 percent on your money, which option should you take and why?

You should accept the $200,000 because the payments are only worth $195,413 to you today. Explanation: PVA = $1,400({1 − [1/(1 + .06/12)(20)(12)]}/(.06/12))PVA = $195,413Difficulty: 2 MediumTopic: Present value - annuityLearning Objective: 06-01 Determine the future and present value of investments with multiple cash flows.Bloom's: AnalyzeAACSB: Analytical ThinkingAccessibility:

The interest earned on both the initial principal and the interest reinvested from prior periods is called:

compound interest

Marko, Incorporated, is considering the purchase of ABC Company. Marko believes that ABC Company can generate cash flows of $4,800, $9,800, and $16,000 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 11 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Company?

$23,977.29

Vimal just purchased an annuity that will pay him $24,000 a year for 25 years. He will receive the first payment today. Given a discount rate is 8.5 percent, how much did Vimal pay for the annuity?

$266,498 The question is solved by calculating the present value of annuity due. This can be solved using a financial calculator by inputting the below into the calculator: The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2ndBGN 2ndSET on the Texas BA II Plus calculator. Enter the below in a financial calculator in BGN mode to compute the future value of ordinary annuity: PMT= 24,000 N= 25 I/Y= 8.5 Press the CPT key and PV to compute the future value of ordinary annuity. The value obtained is 266,498.33. Therefore, the value of the annuity today is $266,498.33.

Javier and Alex plan on retiring 27 years from today. At that time, they plan to have saved the same amount. Javier is depositing $15,000 today at an annual interest rate of 5.2 percent. How will Alex's deposit amount vary from Javier's if Alex also makes a deposit today, but earns an annual interest rate of 6.2 percent? Alex's deposit will need to be ______ than Javier's. (Assume annual compounding on both accounts.)

$3,381.39 less We use the formula:A=P(1+r/100)^nwhereA=future valueP=present valuer=rate of interestn=time period. Hence future value of Duane=$15000*(1.052)^27 =$58,954.40(Approx). For Thad: 58,954.40=P*(1.062)^27 P=58,954.40/(1.062)^27 =$11618.61(Approx). Hence difference=15000-11618.61 =$3381.39(Approx).

What is the future value of $2,968 invested for 9 years at 4.9 percent compounded annually?

$4,565.03 Future value is the method of calculating how much the present value of an asset or cash will be worth at a specific period of time. future value formula = present value × [(1+rateof interest) ^ n] = 2968 × [(1+ 0.049) ^ 9] =2968 × [(1.049) ^9] = 2968 × 1.53808166 = 4565.03

You want to have $82,000 in 17 years to help your child attend college. If you can earn an annual interest rate of 3.8 percent, how much will you have to deposit today?

$43,496.95 Explanation: Present value = Future value/(1+i)^n i = interest rate per period n= number of periods Present value = 82000/1.038^17 = 43,496.95

Aidan deposited $8,500 in an account today. If the account earns 8.5 percent per year, compounded annually, how many years will it take for the account to reach a balance of $138,720?

34.23 years FV = 138720 PV = 8500 r= 8.5%= 0.085 A= P(1+r)^n => 138720=8500*(1.085)^n => 16.32 = (1.085)^n taking log on both sides => ln(16.32) = n*ln(1.085) So n= ln(16.32)/ln(1.085) => n =34.228 = 34.23 years So Option e) is the answer

Howell Corporation deposited $12,000 in an investment account one year ago for the purpose of buying new equipment. Today, it is adding another $15,000 to this account. The company plans on making a final deposit of $10,000 to the account one year from today and plans to purchase the equipment four years from today. Assuming an interest rate of 5.5 percent, how much cash will be available when the company is ready to buy the equipment?

$46,008.30 equal payments paid at the end of regular intervals over a stated time period. JK Mfg. keen on buying new equipment four years from today D1 = Amount deposited in Investment account 1 year ago is $12,000, so number of years for which amount is invested is 5 years D2 =Today they deposited another $15,000 for 4 years D3 = One year fron now, they will agian deposit amount of $10,000 for 3 years to be kept in Investment account. calculating the Future Value at the end of year 4 of all the depsoits:- Future Value = D1(1+r)^5 + D2(1+r)^4 + D3(1+r)^3 where, r = Interest rate = 5.5% Future Value = $12000*(1+0.055)^5 + $15,000*(1+0.055)^4 + $10,000(1+0.055)^3 Future Value = $12,000*1.30696000641 + $15,000*1.23882465062 + $10,000*1.174241375 Future Value = $15683.52 + $18582.37 + $11,742.41 Future Value = $46,008.30 So, cash will be available when the company is ready to buy the equipment is $46,008.30 If you need any clarification, you can ask in comments. If you like my answer, then please up-vote as it will be motivating

Your grandparents would like to establish a trust fund that will pay you and your heirs $175,000 per year forever with the first payment one year from today. If the trust fund earns an annual return of 3.4 percent, how much must your grandparents deposit today?

$5,147,058.82 Amount to be deposited today = Annual Amount to be received / Annual return = $ 175000/3.4% = $ 5147058.82 Answer : $ 5,147,058.82

Your parents are giving you $180 a month for 4 years while you are in college. At an interest rate of .43 percent per month, what are these payments worth to you when you first start college?

$7,791.59 Amount of P = $180 is given each month for n = 4*12 = 48 months Interest rate r = 0.43% per month = 0.0043 Present value of the payments = P[1 - (1+r)-n]/r = 180(1 - 1.0043-48)/0.0043 = $7791.59

A friend agreed to lend you money today. You must repay your friend by making payments of $30 per month for the next six months. The first payment must be paid today. In addition, you must pay 2 percent interest per month. How much total interest will you end up paying your friend?

$8.60

You are paying an EAR of 16.78 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account?

15.61% EAR = ( 1 + APR/12)12 - 1 0.1678 = ( 1 + APR/12)12 - 1 1.1678 = ( 1 + APR/12)12 1.013011 = 1 + APR/12 0.013011 = APR/12 APR = 0.1561 or 15.61 percent

Qiaochu purchased a parcel of land costing $67,900. Today, that land is valued at $64,800. How long has she owned this land if the price has been decreasing by 1.5 percent per year?

3.09 years To find the number of years, we need to put the following values in the financial calculator: I/Y = -1.5; PV = -67,900 PMT = 0; FV = 64,800; Press CPT, then N, which gives us 3.09 So, She owned this land for 3.09 years.

Twenty-one years ago, Marisol set aside $5,000 in case of a financial emergency. Today, that account has increased in value to $18,250. What annually compounded rate of interest is her account earning?

6.36% Future value = Present vlaue*(1+r)^n r = Annually compounded Interest rate n = number of Periods 18250 = 5000*(1+r)^21 r = (18250 / 5000)^(1/21) - 1 Annually compounded interest rate = 6.36%

What is the APR on a loan with a stated rate of 2.35 percent per quarter?

9.40% The annual percentage rate is the rate of return for the whole year instead of just Monthly or Quarterly. Quarterly rate = 2.35% So, Annual Rate = 2.35%*4 = 9.40%

Hayley won a lottery and will receive $1,000 each year for the next 30 years. The current value of these winnings is called the:

Present Value The current value of these winnings is called the present value. Present value is the value today of a amount to be received tommorrow. it is obtained after discounting the interest from the future amount.

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?

You should accept the 2nd offer b/c it has the largest net present value Explanation: Offer A: PV = $89,500Offer B: PV = $35,000 + $70,000/1.1152PV = $91,305.17Difficulty: 2 MediumTopic: Present value - multiple cash flowsLearning Objective: 06-01 Determine the future and present value of investments with multiple cash flows.Bloom's: AnalyzeAACSB: Analytical ThinkingAccessibility:

The interest rate that is most commonly quoted by a lender is referred to as the:

annual percentage rate

Your aunt has promised to give you $5,000 when you graduate from college. You expect to graduate three years from now. If you speed up your plans to enable you to graduate two years from now, the present value of the promised gift will:

increase