Business Finance

The variables in a future value of a lump sum problem include all of the following, except:

Annuity payments

1. What is the future value of $3,058 invested for 10 years at 5.8 percent compounded annually?

[2ND] [CLR TVN] 3058 [PV] 5.8 [I/Y] 10 [N] [CPT] [FV] = 5373.9566

What is the present value of $1,000 to be received in 12 years invested at a rate of 8%?

N=12 I/Y= 8 PV=-1000 [2ND] [CLR TVN] -1000 [PV] 8 [I/Y] 12 [N] [CPT] [FV] = 397.1138

What is the future value of $1,000 invested for 15 years at a rate of 5%?

N=15 I/Y=5 PV= -1000 [2ND] [CLR TVN] -1000 [PV] 5 [I/Y] 15 [N] [CPT] [FV] = 2078.9282

What is the future value of $1,200 invested for 20 years at a rate of 6%?

N=20 I/Y= 6 PV=-1200 [2ND] [CLR TVN] -1200 [PV] 6 [I/Y] 20 [N] [CPT] [FV] = 3848.5626

How would a decrease in the interest rate effect the future value of a lump sum, single amount problem (all other variables remain the same)?

Decrease the Future Value

1. You are going to deposit $20,000 today. You will earn an annual rate of 3.7 percent for 13 years, and then earn an annual rate of 3.1 percent for 16 years. How much will you have in your account in 29 years?

3.7% [2ND] [CLR TVN] 20000 [PV] 3.7 [I/Y] 13 [N] [CPT] [FV] = 32074.0520 3.1% [2ND] [CLR TVN] 32074.0520 [PV] 3.18 [I/Y] 16 [N] [CPT] [FV] = 52274.8113

1. You are going to deposit $3,000 in an account that pays .36 percent interest per month. How much will you have in 6 years?

6 x 12 = 72 to get [N] for monthly interest [2ND] [CLR TVN] 3000 [PV] .36 [I/Y] 72 [N] [CPT] [FV] = 3885.8698

1. Retirement Investment Advisors, Inc., has just offered you an annual interest rate of 6.2 percent until you retire in 40 years. You believe that interest rates will increase over the next year and you would be offered 6.8 percent per year one year from today. If you plan to deposit $19,000 into the account either this year or next year, how much more will you have when you retire if you wait one year to make your deposit?

6.2% [2ND] [CLR TVN] 19,000 [PV] 6.2 [I/Y] 40 [N] [CPT] [FV] = 210,733.8351 6.8% [2ND] [CLR TVN] 19000 [PV] 6.8 [I/Y] 39 [N] [CPT] [FV] = 247190.8870

1. You have just deposited $9,000 into an account that promises to pay you an annual interest rate of 6.1 percent each year for the next 7 years. You will leave the money invested in the account and 15 years from today, you need to have $25,650 in the account. What annual interest rate must you earn over the last 8 years to accomplish this goal?

7 years [2ND] [CLR TVN] 9000 [PV] 6.1 [I/Y] 7 [N] [CPT] [FV]= 13622.2924 8 years [2ND] [CLR TVN] -13622.2924 [PV] 25650 [FV] 8 [N] [CPT] [I/Y]= 8.2317%

1. You currently have $6,200. First United Bank will pay you an annual interest rate of 7.3, while Second National Bank will pay you an annual interest rate of 8.6. How many fewer years must you wait for your account value to grow to $21,100 at Second National Bank?

7.3 % [2ND] [CLR TVN] -6200 [PV] 21100 [FV] 7.3 [I/Y] [CPT] [N] 17.3822 8.6% [2ND] [CLR TVN] -6200 [PV] 21100 [FV] 8.6 [I/Y] [CPT] [N] 14.8449 Difference 17.3822 - 14.8449 = 2.5373 years

The variables in a present value of a lump sum problem include all of the following, except:

Free Cash Flow

The variable that you are solving for in a future value of a lump sum problem is:

Future Value

How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)?

Increase the present value.

1. You made an investment of $16,500 into an account that paid you an annual interest rate of 2.8 percent for the first 7 years and 7.2 percent for the next 14 years. What was your annual rate of return over the entire 21 years?

Part 1 2.8% [2ND] [CLR TVN] 16500 [PV] 2.8 [I/Y] 7 [N] [CPT] [FV] = 20018.6943 7.2% [2ND] [CLR TVN] 20018.6943 [PV] 7.2 [I/Y] 14 [N] [CPT] [FV] = 52986.1961 Part 2 [2ND] [CLR TNV] -16500 [PV] 52986.1961 [FV] 21 [N] [CPT] [I/Y] = 5.7128 %

The variables in a future value of a lump sum problem include all of the following, except:

Payments

The variables in a present value of a lump sum problem include all of the following, except:

Payments

The variable that you are solving for in a present value of a lump sum problem is:

Present Value

1. Your sister just deposited $12,000 into an investment account. She believes that she will earn an annual return of 10.1 percent for the next 8 years. You believe that you will only be able to earn an annual return of 9.4 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 8 years?

Sister [2ND] [CLR TVN] 12000 [PV] 10.1 [I/Y] 8 [N] [CPT] [FV]= 25910.7389 Me [2ND] [CLR TVN] 25910.7389 [FV] 9.4 [I/Y] 8 [N] [CPT] [PV]= 12628.1933 Difference= 12628.1933-12000= 628.1933

1. You purchased a bond at a price of $700. In 20 years when the bond matures, the bond will be worth $5,000. It is exactly 12 years after you purchased the bond and you can sell the bond today for $3,550. If you hold the bond until it matures, what annual rate of return will you earn from today?

[2ND] [CLR TNV] -3550 [PV] 5000 [FV] 8 (20-12) [N] [CPT] [I/Y] = 4.3741 %

1. You are going to deposit $2,500 in an account that pays .51 percent interest per quarter. How much will you have in 5 years?

[2ND] [CLR TVN] 2500 [PV] .51 [I/Y] 20 [N] [CPT] [FV] = 2767.7411

1. You need to have $25,000 for a down payment on a house 7 in years. If you can earn an annual interest rate of 4.3 percent, how much will you have to deposit today?

[2ND] [CLR TVN] 25000 [FV] 4.3 [I/Y] 7 [N] [CPT] [PV] = 18618.7212

1. Five years from today, you plan to invest $3,400 for 11 additional years at 5.6 percent compounded annually. How much will you have in your account 16 years from today?

[2ND] [CLR TVN] 3400 [PV] 5.6 [I/Y] 11 [N] [CPT] [FV] = 6191.3024

1. A company has a pension liability of $460,000,000 that it must pay in 29 in years. If it can earn an annual interest rate of 4.2 percent, how much must it deposit today to fund this liability?

[2ND] [CLR TVN] 460000000 [FV] 4.2 [I/Y] 29 [N] [CPT] [PV] = 139506351.80

1. Today, your dream car costs $54,500. You feel that the price of the car will increase at an annual rate 2.4 percent. If you plan to wait 4 years to buy the car, how much will it cost at that time?

[2ND] [CLR TVN] 54500 [PV] 2.4 [I/Y] 4 [N] [CPT] [FV] = 59923.3837

1. You want to have $84,000 in 16 years to help your child attend college. If you can earn an annual interest rate of 4 percent, how much will you have to deposit today?

[2ND] [CLR TVN] 84000 [FV] 4 [I/Y] 16 [N] [CPT] [PV] = 44848.2868

1. The most recent census for a city indicated that there were 971,661 residents. The population of the city is expected to increase at an annual rate of 4.2 percent each year for the next 8 years. What will the population be at that time?

[2ND] [CLR TVN] 971661 [PV] 4.2 [I/Y] 8 [N] [CPT] [FV] = 1350381.636

1. You need to have $32,000 in 7 years. You can earn an annual interest rate of 3 percent for the first 4 years, and 3.6 percent for the next 3 years. How much do you have to deposit today?

a. (3 x 4) + (3.6 x 3) = 22.8/7 (years) 3.2571 avg I/Y [2ND] [CLR TVN] 32000 [FV] 3.2571 [I/Y] 7 [N] [CPT] [PV] = approx. 25568.7355 on hw 25569.48

1. You need to have $32,250 in 17 years. You can earn an annual interest rate of 4 percent for the first 5 years, 4.6 percent for the next 4 years, and 5.3 percent for the final 8 years. How much do you have to deposit today?

a. (4 x 5) + (4.6 x 4) + (5.3 x 8) = 80.8/17 (years) 4.7529 avg I/Y [2ND] [CLR TVN] 32250 [FV] 4.7529 [I/Y] 17 [N] [CPT] [PV] = approx. 14645.5871 on hw 14649.05

1. A small business has determined that the machinery they currently use will wear out in 17 years. To replace the new machine when it wears out, the company wants to establish a savings account today. If the interest rate on the account is 1.9 percent compounded quarterly and the cost of the machinery will be $340,000, how much will the company have to deposit today?

a. 17 x 4 = 68 for N [2ND] [CLR TVN] 340000 [FV] 1.9 [I/Y] 68 [N] [CPT] [PV] = 94544.0940

The winner of the first annual Tom Morris Golf Invitational won $105 in the competition which was held in 1899. In 2015, the winner received $1,460,000. If the winner's purse continues to increase at the same interest rate, how much will the winner receive in 2050?

a. 2015-1899= 116 years [2ND] [CLR TVN] -105 [PV] 1460000 [FV] 116 [N] [CPT] [I/Y]= 8.5718% 2050-1899=151 years [2ND] [CLR TVN] 105 [PV] 8.5718 [I/Y] 151 [N] [CPT] [FV]= Approx: 25969407.33 on HW 25968406.94

1. Beatrice invests $1,300 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually?

a. First find Simple interest Simple interest = 1300 x.03 x 4= 156 = 1300 +156 = 1456 Compound interest = [2ND] [CLR TVN] 1300 [PV] 3 [I/Y] 4 [N] [CPT] [FV] = 1463.1615 Difference = 1463.1615 - 1456 = 7.1615

1. You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $2,600 today and both accounts have an annual interest rate of 5 percent. How much more interest will you receive in the 8th year in the account that pays compound interest?

a. First find Simple interest Simple interest = 2600 x .05 x 1 = 156 = 1300 +156 = 1456 Compound interest = Year 8 [2ND] [CLR TVN] 2600 [PV] 5 [I/Y] 8 [N] [CPT] [FV] = 3841.3842 Year 7 [2ND] [CLR TVN] 2600 [PV] 5 [I/Y] 7 [N] [CPT] [FV] = 3658.4611 Compound interest for year 8 = 3841.3842 - 3658.4611 = 182.9231 How much more = 182.9231 - 130 = 52.9231

1. What is the present value of $1,200 to be received in 18 years invested at a rate of 5%?

a. N=18 I/Y= 5 FV=1200 [2ND] [CLR TVN] 1200 [FV] 5 [I/Y] 12 [N] [CPT] [PV] = 498.6248

1. Thomas invests $107 in an account that pays 4 percent simple interest. How much money will Thomas have at the end of 6 years?

a. Simple interest = principal X interest X time = 107 x (.04 x 6) = 25.68 =107 + 25.68 = 132.68

1. An investor who was not as astute as he believed invested $284,000 into an account 8 years ago. Today, that account is worth $219,600. What was the annual rate of return on this account?

a. [2ND] [CLR TNV] -284000 [PV] 219600 [FV] 8 [N] [CPT] [I/Y] = - 3.1635 %

1. Rick deposited $3,150 into an account 8 years ago for an emergency fund. Today, that account is worth $4,290. What annual rate of return did Rick earn on this account assuming no other deposits and no withdrawals?

a. [2ND] [CLR TNV] -3150 [PV] 4290 [FV] 8 [N] [CPT] [I/Y] = 3.9366 %

1. You expect to receive $2,900 upon your graduation and will invest your windfall at an interest rate of .39 percent per quarter until the account is worth $4,600. How many years do you have to wait until you reach your target account value?

a. [2ND] [CLR TVN] --2900 [PV] 4600 [FV] .39 [I/Y] [CPT] [N] = 118.5243/4 (quarters) = 29.6311 YEARS

1. You have $12,500 and will invest the money at an interest rate of .36 percent per month until the account is worth $19,000. How many years do you have to wait until you reach your target account value?

a. [2ND] [CLR TVN] -12500 [PV] 19000 [FV] .36 [I/Y] [CPT] [N] = 116.5177/12 (months) = 9.7098 YEARS

1. Maxxie purchased a tract of land for $29,500. Today, the same land is worth $45,100. How many years have passed if the price of the land has increased at an annual rate of 5.7 percent?

a. [2ND] [CLR TVN] -29500 [PV] 45100 [FV] 5.7 [I/Y] [CPT] [N] 7.6575 YEARS