TVM Finance Exam Guide

Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 a month for the next 20 years. What is the rate of return on this investment? (A) 1.88% (B) 3.75% (C) 2.45% (D) 2.47%

(A) 1.88%

Island News purchased a piece of property for $2 million. The firm paid a down payment of 20 percent in cash and financed the balance. The loan terms require monthly payments for 25 years at an APR of 5.5 percent compounded monthly. What is the amount of each mortgage payment? (A) $9,825.40 (B) $9,253.92 (C) $88,000.01 (D) $12,281.75

(A) $9,825.40

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at Year 5 and an annual percentage rate of 10 percent? (A) Annual. (B) Semi-Annual. (C) Monthly. (D) Daily.

(A) Annual.

Your parents are about to buy a new 2018 Subaru Outback Limited which will cost approximately $35,000. After paying tax, title, license and making a down payment, your parents will need to borrow $27,500 to complete the purchase of their new Outback and are presented with two options. Your parents want to repay their car loan over 60 months. Option one is 0.0% APR financing for 60 months. The second option is $2,000 cash back which would be used as an additional down payment reducing the loan amount by this $2,000 cash back. Your parents discover that they can get 2.29% APR financing for 60 months if they elect the second (cash back) option. What is the 0% APR monthly payment minus the $2,000 cash back monthly payment for your parents' situation (i.e. if 0% APR payment is higher difference is positive)? (A) -$5.66 (B) +$8.13 (C) +$10.87 (D) -$27.18

(B) +$8.13

Suppose you are buying your first condo for $220,000 in 5 years. You will use two funding sources. First, you will use your current savings of $9,313.82 invested in an account that earns 10 percent com- pounded annually as a down payment. Second, you will arrange to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5 percent nominal interest rate, with the first payment due in the end of the month. What will your monthly payments be? (A) $1,295.74 (B) $1,023.63 (C) $1,373.48 (D) $1,580.80

(A) $1,295.74

Paige wants to have $40,000 for a down payment on a house five years from now. She can either deposit one lump sum today or wait one year and deposit a lump sum then. Assume an interest rate of 3.5 percent, compounded annually. How much additional money must she deposit if she waits for one year rather than making the deposit today? (A) $1.178.86 (B) $1,001.98 (C) $986.13 (D) $1,020.18

(A) $1.178.86

Aidan can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, what is the most he can afford to borrow? (A) $11,697.88 (B) $11,750.00 (C) $12,348.03 (D) $10,400.00

(A) $11,697.88

It's your 20th birthday and you have decided that on each of your next 40 birthdays you will contribute $6,000 to a Roth IRA account. If you earn an 8% annual rate of return both before and after your retirement at age 60, how much annual retirement income will your IRA provide for you during your first 35 years of retirement? (A) $133,367 (B) $1,678,686 (C) $1,554,339 (D) $123,488

(A) $133,367

Rahul is scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 percent. What is the difference in the present value if these payments are paid at the beginning of each year rather than at the end of each year? (A) $2,170.39 (B) $2,511.07 (C) $2,021.18 (D) $2,027.94

(A) $2,170.39

You will receive $15,000 in two years when you graduate. You plan to invest this at an annual interest rate of 6.5 percent, compounded annually. How much money will you have 8 years from now? (A) $21,887.13 (B) $19,381.16 (C) $24,824.94 (D) $23,209.19

(A) $21,887.13

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt? (A) $27,016.84 (B) $28,299.95 (C) $21,400.33 (D) $22,218.09

(A) $27,016.84

Calculate the monthly payment for a 20-year mortgage on a $3.5 million building at a 7.5% interest rate. Assume that the entire building is financed and that payments are made at the end of each month, starting at the end of the first month and ending at the end of the last month. (A) $28,195.76 (B) $28,020.63 (C) $61,947.83 (D) $36,458.33

(A) $28,195.76

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.) (A) $3,381.39 less (B) $4,274.12 less (C) $3,417.09 more (D) $4,118.42 more

(A) $3,381.39 less

You want to buy a Nissan 300ZX on your 27th birthday. These cars currently sell for $30,000. You believe that the price will increase by 5 percent per year until you are ready to buy. You can presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years? (A) $3,933.93 (B) $4,945.57 (C) $3,450.82 (D) $6,030.43

(A) $3,933.93

As part of his new 10-year contract with the St. Louis Cardinals, Albert Pulojs will have $5M of his salary at the end of each of the next 10 years deferred at 6% compounded annually. At his retirement at the end of this 10-year contract, Albert wants to make 40 equal beginning-of-the-year withdrawals from his deferred salary account. How large will Albert's annual retirement withdrawal be assuming the deferred salary account continues to earn 6% compounded annually? (A) $4.13M (B) $4.38M (C) $5.08M (D) $3.52M

(A) $4.13M

You are negotiating to make a 7-year loan of $27,500 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. You regard 8% as an appropriate rate of return on a 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X? (A) $5,683.99 (B) $5,513.47 (C) $5,172.43 (D) $5,740.83

(A) $5,683.99

ou just obtained a loan of $17,200 with monthly payments for three years at 5.5 percent interest compounded monthly. What is the amount of each payment? (A) $519.37 (B) $467.43 (C) $439.96 (D) $1,107.10

(A) $519.37

Bob Belcher, proprietor of Bob's Burgers, plans to make 15 semi-annual deposits of $3,000 beginning today and ending 7 years from now into an account that will pay a 7% nominal annual rate compounded semi-annually. How much will Bob have in this account 7 years from today after he makes his last deposit? (A) $57,887 (B) $53,031 (C) $54,887 (D) $59,913

(A) $57,887

Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease? (A) $6,232.80 (B) $10,331.03 (C) $9,197.74 (D) $7,203.14

(A) $6,232.80

A scholarship will pay you $150 at the end of each month for four years while you attend college. At a discount rate of 3.7 percent, what are these payments worth to you on the day you enter college? (A) $6,682.99 (B) $6,539.14 (C) $6,608.87 (D) $6,870.23

(A) $6,682.99

The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years? (A) $67,485.97 (B) $70,459.07 (C) $69,068.18 (D) $67,233.84

(A) $67,485.97

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.) (A) $89.70 (B) $92.19 (C) $88.78 (D) $90.21

(A) $89.70

(47) You want to be a millionaire when you retire in 30 years and expect to earn 8.5 percent compounded monthly. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month? (A) $989.10 (B) $841.15 (C) $1,046.80 (D) $947.22

(A) $989.10

The Rodriquez family is determined to purchase a $250,000 home without incurring any debt. The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent compounded quarterly. How long will it be until the family can purchase a home? (A) 14.85 Years (B) 23.09 Years (C) 35.46 Years (D) 48.82 Years

(A) 14.85 Years

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?(A) 15.61% (B) 14.98% (C) 15.75% (D) 16.35%

(A) 15.61%

You just received an offer in the mail to transfer the $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 7.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card? (A) 2.63 Payments (B) 2.48 Payments (C) 2.86 Payments (D) 2.79 Payments

(A) 2.63 Payments

At 5 percent annually compounded interest, how long would it take to triple your money? (A) 22.52 Years (B) 26.55 Years (C) 25.64 Years (D) 24.87 Years

(A) 22.52 Years

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? (A) 34.23 Years (B) 29.78 Years (C) 46.55 Years (D) 16.32 Years

(A) 34.23 Years

Freida Farmer, 78 years young, from Erie, PA has the winning Powerball lottery numbers which will pay out $10M at the beginning of each of the next 30 years. Before claiming her prize, Dependable Insurance Company offers Frieda $170M today in exchange for her winning lottery ticket and prize payout. What rate of return would Dependable Insurance earn if Frieda accepts their offer? (A) 4.51% (B) 4.99% (C) 4.14% (D) 4.73%

(A) 4.51%

Jane has just won a lottery with a reported prize of $40M. However, this reported prize is just the sum of the 20 beginning-of-the-year payments of $2,000,000 per year, and this particular lottery doesn't offer an upfront cash option. This presents a problem for Jane because she wants to use her lottery winnings to fund her dream to build a Wildebeest Sanctuary right away and she would need more than the initial $2,000,000 lottery prize payment. Jane decides to put her entire lottery prize annuity up for bid. Several insurance and finance companies respond, and Prairie Insurance Company has the highest bid of $27M, which is accepted by Jane. What annual rate of return would the company earn with their bid? (A) 4.59% (B) 6.15% (C) 5.62% (D) 4.07%

(A) 4.59%

You plan to invest $10,000 in a certificate of deposit (CD) for 14 years. For the first six years, you invest in a CD that pays an annual interest rate of 6 percent, while for the remaining eight years you invest in a CD that pays an annual interest rate of 4 percent. What is the equivalent annual rate of return over the entire 14 years? (A) 4.85% (B) 5.02% (C) 4.75% (D) 4.92%

(A) 4.85%

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? (A) 5.61% (B) 5.79% (C) 5.50% (D) 6.25%

(A) 5.61%

You want to borrow $27,500 and can afford monthly payments of $650 for 48 months, but no more. Assume monthly compounding. What is the highest APR rate you can afford? (A) 6.33% (B) 6.67% (C) 5.82% (D) 7.18%

(A) 6.33%

What is the EAR if a bank charges you an APR of 7.65 percent compounded quarterly? (A) 7.87% (B) 8.11% (C) 8.38% (D) 8.02%

(A) 7.87%

All else constant, which one of the following will result in the lowest present value of a lump sum? (A) 8 percent interest for 10 years (B) 8 percent interest for 5 years (C) 6 percent interest for 10 years (D) 6 percent interest for 5 years

(A) 8 percent interest for 10 years

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? (A) 83.77 (B) 89.46 (C) 91.12 (D) 97.30

(A) 83.77

What is the APR on a loan with a stated rate of 2.35 percent per quarter? (A) 9.40% (B) 8.69% (C) 8.38% (D) 8.90%

(A) 9.40%

Which one of the following statements related to annuities and perpetuities is correct? (A) A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal. (B) An ordinary annuity is worth more than an annuity due given equal annual cash flows for 10 years at 7 percent interest compounded annually. (C) The present value of a perpetuity cannot be computed but the future value can. (D) Perpetuities are finite but annuities are not.

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

You are comparing two annuities that offer regular payments of $2,500 for five years and pay 0.75 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) Annuity B has a smaller present value than Annuity A. (B) Annuity A has a smaller future value than Annuity B. (C) These two annuities have both equal present and equal future values. (D) Annuity B is an annuity due.

(A) Annuity B has a smaller present value than Annuity A.

Which one of the following actions will increase the present value of an amount to be received sometime in the future? (A) Decrease in the interest rate (B) Decrease in the future value (C) Increase in the discount rate (D) Decrease in both the future value and the number of time periods

(A) Decrease in the interest rate

Caroline is going to receive an award of $20,000 six years from now. Jiexin is going to receive an award of $20,000 nine years from now. Which one of the following statements is correct if both individuals apply a discount rate of 7 percent? (A) In today's dollars, Caroline's award is worth more than Jiexin's. (B) Jiexin's award is worth more today than Caroline's award. (C) In future dollars, Jiexin's award is worth more than Caroline's award. (D) Twenty years from now, the value of Caroline's award will equal the value of Jiexin's award.

(A) In today's dollars, Caroline's award is worth more than Jiexin's.

Four years ago, Lucas invested $500. Three years ago, Matt invested $600. Today, these two invest- ments are each worth $800. Assume each account continues to earn its respective rate of return and interest is compounded annually. Which one of the following statements is correct concerning these investments? (A) One year ago, Lucas's investment was worth less than Matt's investment. (B) Three years from today, Matt's investment will be worth more than Lucas's investment. (C) Matt earns a higher rate of return than Lucas. (D) Lucas has earned an average annual interest rate of 12.64 percent.

(A) One year ago, Lucas's investment was worth less than Matt's investment.

Chris has three options for settling an insurance claim. Option A will provide $1,500 a month for 6 years. Option B will pay $1,025 a month for 10 years. Option C offers $85,000 as a lump sum payment today. The applicable discount rate is 6.8 percent compounded monthly. Which option should Chris select, and why, if he is only concerned with the financial aspects of the offers? (A) Option B: It has the largest value today. (B) Option B: It pays the greatest number of payments. (C) Option A: It provides the largest monthly payment. (D) Option C: It is all paid today.

(A) Option B: It has the largest value today.

Project X has cash flows of $8,500, $8,000, $7,500, and $7,000 for Years 1 to 4, respectively. Project Y has cash flows of $7,000, $7,500, $8,000, and $8,500 for Years 1 to 4, respectively. Which one of the following statements is true concerning these two projects given the same positive discount rate for both projects? (No calculations needed.) (A) Project X has both a higher present and a higher future value than Project Y. (B) Project Y has a higher present value than Project X. (C) Both projects have the same future value at the end of Year 4. (D) Both projects have the same value at Time 0.

(A) Project X has both a higher present and a higher future value than Project Y.

Which one of the following statements related to loan interest rates is correct? (A) When comparing loans you should compare the effective annual rates. (B) The annual percentage rate considers the compounding of interest. (C) Regardless of the compounding period, the effective annual rate will always be higher than the annual percentage rate. (D) The more frequent the compounding period, the lower the effective annual rate given a fixed annual percentage rate.

(A) When comparing loans you should compare the effective annual rates.

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:(A) could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest. (B) will earn simple interest on his savings every year for four years. (C) will earn the same amount of interest each year for four years. (D) could earn more interest on this account if the interest earnings were withdrawn annually.

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

Your bank offers to lend you $230,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2? (A) $17,503 (B) $18,232 (C) $15,497 (D) $14,403

(B) $18,232

Springfield mogul Montgomery Burns, age 75, wants to retire at age 90. Once Mr. Burns retires, he wants to withdraw $500M at the beginning of each year for 20 years from a special off-shore account that will pay 18% annually. In order to fund his retirement, Mr. Burns will make a $150M deposit today plus 15 equal end-of-the-year deposits in this same special account that will pay 18% annually. How large of an annual deposit must be made to fund Mr. Burns retirement plans? (A) $18.93M (B) $22.34M (C) $34.45M (D) $25.67M

(B) $22.34M

Last Tuesday's Mega Millions prize was estimated to be $122M. The winner can elect a cash option of $75M today or a 26-year annuity with annual beginning-of-the-period payments of $4.69M. What is the difference between today's present value of the cash option and annuity payout at 5% compounded annually? Calculate your answer as PV(Cash Option) - PV(Annuity Payout). (A) +$0.42M (B) +$4.21M (C) +$7.58M (D) -$3.79M

(B) +$4.21M

Your subscription to "Investing Wisely Weekly" is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $930, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? (A) 13.59 (B)16.57 (C) 20.72 (D) 16.91

(B)16.57

Your uncle will sell you his bicycle shop for $240,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be? (A) $4,476.55 (B) $3,675.48 (C) $4,712.16 (D) $4,146.70

(C) $4,712.16

Steve and Ed are cousins who were both born on the same day, and both turning 25 in a year. Their grandfather began putting $3,800 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather will make 40 more $3,800 payments until a 46th and final payment is made on Steve's 65th birthday. Until now, the grandfather has not given Ed anything. However, he just decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed in a year, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday? (Hint: Both are Ordinary Annuities) (A) $5,153 (B) $5,833 (C) $5,663 (D) $5,889

(C) $5,663

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that is expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. (A) $58,601 (B) $68,179 (C) $64,932 (D) $61,686

(C) $64,932

You want to create an endowment to fund a football scholarship, which pays $25,000 per year, forever, how much money must be set aside today if the rate of interest is 4.7%? (A) $736,857 (B) $517,698 (C) $682,477 (D) $531,915

(D) $531,915

You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $2,100 today and both accounts have an annual interest rate of 5%. How much more interest will you receive in the 10th year in the account that pays compound interest? (A) $70.74 (B) $71.56 (C) $75.05 (D) $57.89

(D) $57.89

(1) Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan? (A) 17.81% (B) 17.52% (C) 15.08% (D) 14.36%

(D) 14.36%

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 21.75%, with interest paid monthly, what is the card's Effective Annual Rate (EAR)? (A) 21.89% (B) 24.78% (C) 24.30% (D) 24.05%

(D) 24.05%