Time value of money

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what is time value of money? It is the idea that money invested today has more value that the same invested later
On January 1, 1985, a graduate student developed a financial plan that would provide enough money at the end of his graduate work (January 1, 1990) to open a business of his own. His plan was to deposit $8,000 per year, starting immediately, into an account paying 10% compounded annually. His activities proceeded according to plan except that at the end of his third year he withdrew $5,000 to take a Caribbean cruise, at the end of the fourth year he withdrew $5,000 to buy a used Camaro, and at the end of the fifth year he had to withdraw $5,000 to pay to have his dissertation typed. His account, at the end of the fifth year, will be less than the amount he had originally planned on by how much? $16,550
If you buy a factory for $250,000 and the terms are 20% down, the balance to be paid off over 30 years at a 12% rate of interest on the unpaid balance, what are the 30 equal annual payments? $24,828.73
You plan on working for 10 years and then leaving for the Alaskan back country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5 years. In addition, your family has given you a $5,000 graduation gift. If you put the gift and your future savings in an account paying 8% compounded annually, what will your 'stake' be when you leave for the wilderness 10 years hence? $31,147.50
Visser Distributors is financing a new truck with a loan of $10,000 to be repaid in 5 annual installments of $2,505. What annual interest rate is the company paying? 8%
If $100 is placed into an account that earns a nominal 4% compounded quarterly, what will it be worth 5 years from today? $122.05
You plan on working for 10 years and then leaving for the Alaskan back country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5 years. In addition, your family has given you a $5,000 graduation gift. If you put the gift and your future savings in an account paying 8% compounded annually, what will your 'stake' be when you leave for the wilderness 10 years hence? $31,147.50
Suppose you have $2 million in a 2-year account paying a 6% nominal rate, compounded annually. Another bank offers you an account for 2 years paying a 6% nominal rate, but compounded bimonthly (that is, 6 times a year). If you move your account, how much additional interest will you earn over the 2 years? $6,450.06
You have the opportunity to buy a perpetuity paying $1,000 annually. Your demanded rate of return on this investment is 15%. You would be essentially indifferent to buying or not buying the investment if it were offered at what price? $6,666.67
You have decided to deposit your scholarship money ($1,000) in a savings account paying 8% interest, compounded quarterly. Eighteen months later, you decide to go to the mountains rather than school and you close out your account. How much money will you receive? $1,126.16
Your 69-year old aunt has savings of $35,000. She has made arrangements to enter a home for the aged upon reaching the age of 80. Before going into the home, she wants to decrease the account balance by a constant amount each year for ten years, with a zero balance remaining. How much can she withdraw each year if she earns 6 percent annually on her savings? Her first withdrawal would be one year from today $4,755.37
A rich aunt promises you $35,000 exactly 5 years after you graduate from college. What is the value of the promised $35,000 if you could negotiate payment upon graduation? Assume an interest rate of 12 percent. $19,859.94
John Roberts is retiring one year from today. How much should John currently have in a retirement account earning 10 percent interest to guarantee withdrawals of $25,000 per year for 10 years? $153,615
You place $5,000 in your credit union at an annual interest rate of 12 percent compounded monthly. How much will you have in 2 years if all interest remains in the accounts? $6,348.67
According to a local department store, the store charges its customers 1% per month on the outstanding balances of their charge accounts. What is the effective annual rate on such customer credit? Assume the store recalculates your account balance at the end of each month 12.68%
You have agreed to pay a creditor $5,000 one year hence, $4,000 two years hence, $3,000 three years hence, $2,000 four years hence, and a final payment of $1,000 five years from now. Due to budget considerations you would like to make five equal annual payments to satisfy your contract. If the agreed upon interest is 5% effective per year, what should the equal annual payments be? $3,097.43
You have purchased a new sailboat and have the option of paying the entire $8,000 now or making equal, annual payments for the next 4 years, the first payment due one year from now. If your time value of money is 7 percent, what would be the largest amount for the equal, annual payments that you would be willing to undertake? $2,361.83
You are 35 years old and wish to provide for your old age. Suppose you invest $1,000 per year at an effective rate of 5 percent per year for the next 25 years, with the first deposit beginning one year hence. Beginning one year after your last $1,000 deposit you start withdrawing $X per year for the next 20 years. How large must $X be in order to use up all of your funds? $3,829.74
How much would you pay for a joint venture that is expected to yield $20,000 per year for 5 years, and then $50,000 per year for the next 10 years, but will require an expenditure of $100,000 to terminate the venture at the end of its productive life? Assume that you require a 20 percent return on the investment because of its high risk. $137,565
What is the present value of an investment that promises to pay $10,000 for the first five years and $20,000 for the second five years if the discount rate is 18 percent? $58,610
Mr. Lewis, age 29, wants to begin planning for his retirement at age 65. Upon retiring, he wants to be able to withdraw $15,000 per year on each birthday for 10 years. The first withdrawal will be on his 66th birthday. He will receive a large inheritance on his 30th birthday in two weeks, and he wants to know how much he needs to invest on that day to be able to attain his retirement income. He will invest the money in an account paying 10 percent annual interest for the life of the investment. How much does he need to deposit on his 30th birthday? $3,280
If you have $5,436 in an account that has been paying an annual rate of 10%, compounded continuously, since you deposited some funds 10 years ago, how much was the original deposit? $1999.79
In 1975, its first year of operations, The Coffee Mill had earnings per share (EPS) of $0.26. Four years later, in 1978, EPS was up to $0.38, and 7 years later, in 1985, EPS was up to $0.535. It appears that the first 4 years represented an unusual growth situation and that since then a more normal growth rate has been sustained. What are the two rates of growth? 10% and 5% respectively

what is time value of money?

On January 1, 1985, a graduate student developed a financial plan that would provide enough money at the end of his graduate work (January 1, 1990) to open a business of his own. His plan was to deposit $8,000 per year, starting immediately, into an account paying 10% compounded annually. His activities proceeded according to plan except that at the end of his third year he withdrew $5,000 to take a Caribbean cruise, at the end of the fourth year he withdrew $5,000 to buy a used Camaro, and at the end of the fifth year he had to withdraw $5,000 to pay to have his dissertation typed. His account, at the end of the fifth year, will be less than the amount he had originally planned on by how much?

If you buy a factory for $250,000 and the terms are 20% down, the balance to be paid off over 30 years at a 12% rate of interest on the unpaid balance, what are the 30 equal annual payments?

You plan on working for 10 years and then leaving for the Alaskan back country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5 years. In addition, your family has given you a $5,000 graduation gift. If you put the gift and your future savings in an account paying 8% compounded annually, what will your 'stake' be when you leave for the wilderness 10 years hence?

Visser Distributors is financing a new truck with a loan of $10,000 to be repaid in 5 annual installments of $2,505. What annual interest rate is the company paying?

If $100 is placed into an account that earns a nominal 4% compounded quarterly, what will it be worth 5 years from today?

You plan on working for 10 years and then leaving for the Alaskan back country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5 years. In addition, your family has given you a $5,000 graduation gift. If you put the gift and your future savings in an account paying 8% compounded annually, what will your 'stake' be when you leave for the wilderness 10 years hence?

Suppose you have $2 million in a 2-year account paying a 6% nominal rate, compounded annually. Another bank offers you an account for 2 years paying a 6% nominal rate, but compounded bimonthly (that is, 6 times a year). If you move your account, how much additional interest will you earn over the 2 years?

You have the opportunity to buy a perpetuity paying $1,000 annually. Your demanded rate of return on this investment is 15%. You would be essentially indifferent to buying or not buying the investment if it were offered at what price?

You have decided to deposit your scholarship money ($1,000) in a savings account paying 8% interest, compounded quarterly. Eighteen months later, you decide to go to the mountains rather than school and you close out your account. How much money will you receive?

Your 69-year old aunt has savings of $35,000. She has made arrangements to enter a home for the aged upon reaching the age of 80. Before going into the home, she wants to decrease the account balance by a constant amount each year for ten years, with a zero balance remaining. How much can she withdraw each year if she earns 6 percent annually on her savings? Her first withdrawal would be one year from today

A rich aunt promises you $35,000 exactly 5 years after you graduate from college. What is the value of the promised $35,000 if you could negotiate payment upon graduation? Assume an interest rate of 12 percent.

John Roberts is retiring one year from today. How much should John currently have in a retirement account earning 10 percent interest to guarantee withdrawals of $25,000 per year for 10 years?

You place $5,000 in your credit union at an annual interest rate of 12 percent compounded monthly. How much will you have in 2 years if all interest remains in the accounts?

According to a local department store, the store charges its customers 1% per month on the outstanding balances of their charge accounts. What is the effective annual rate on such customer credit? Assume the store recalculates your account balance at the end of each month

You have agreed to pay a creditor $5,000 one year hence, $4,000 two years hence, $3,000 three years hence, $2,000 four years hence, and a final payment of $1,000 five years from now. Due to budget considerations you would like to make five equal annual payments to satisfy your contract. If the agreed upon interest is 5% effective per year, what should the equal annual payments be?

You have purchased a new sailboat and have the option of paying the entire $8,000 now or making equal, annual payments for the next 4 years, the first payment due one year from now. If your time value of money is 7 percent, what would be the largest amount for the equal, annual payments that you would be willing to undertake?

You are 35 years old and wish to provide for your old age. Suppose you invest $1,000 per year at an effective rate of 5 percent per year for the next 25 years, with the first deposit beginning one year hence. Beginning one year after your last $1,000 deposit you start withdrawing $X per year for the next 20 years. How large must $X be in order to use up all of your funds?

How much would you pay for a joint venture that is expected to yield $20,000 per year for 5 years, and then $50,000 per year for the next 10 years, but will require an expenditure of $100,000 to terminate the venture at the end of its productive life? Assume that you require a 20 percent return on the investment because of its high risk.

What is the present value of an investment that promises to pay $10,000 for the first five years and $20,000 for the second five years if the discount rate is 18 percent?

Mr. Lewis, age 29, wants to begin planning for his retirement at age 65. Upon retiring, he wants to be able to withdraw $15,000 per year on each birthday for 10 years. The first withdrawal will be on his 66th birthday. He will receive a large inheritance on his 30th birthday in two weeks, and he wants to know how much he needs to invest on that day to be able to attain his retirement income. He will invest the money in an account paying 10 percent annual interest for the life of the investment. How much does he need to deposit on his 30th birthday?

If you have $5,436 in an account that has been paying an annual rate of 10%, compounded continuously, since you deposited some funds 10 years ago, how much was the original deposit?

In 1975, its first year of operations, The Coffee Mill had earnings per share (EPS) of $0.26. Four years later, in 1978, EPS was up to $0.38, and 7 years later, in 1985, EPS was up to $0.535. It appears that the first 4 years represented an unusual growth situation and that since then a more normal growth rate has been sustained. What are the two rates of growth?

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