Sample Problems—Time Value of Money
1. Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted annual rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charges by the two banks? 2. In 1889, Vincent Van Gogh’s painting, “Sunflowers”, sold for $125. In 1987 it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, how much would your average annually compounded rate of return have been—n=98. 3. You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?

4. Smokey Stack smokes a pack of cigarettes a day. Each pack of cigarettes costs $2.25. Smokey, having learned about the time value of money in his finance class, is wondering how much money he could accumulate if he quit smoking and invested the money. Assuming, the amount saved each year is invested at the end of the year at a 8% rate of return, how much could Smokey accumulate during the next 40 years (assume a 365-day year and that the cost of cigarettes stays constant over the 40 year period)

5. Your brother-in-law borrowed $1,000 from you 10 years ago and then disappeared. Yesterday he returned and expressed a desire to pay back the loan, including the interest that accrued since he borrowed the money. Assuming that you had agreed to charge him 7%, and assuming that he wishes to make five equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to extinguish the debt? (Assume the loan continues to accrue interest at 7% per...

...Abstract
In this paper, Team C will discuss the concept of the timevalue of money and the importance of this concept in business. Also, we will provide a demonstration of the use of the formula used to calculate the present and future values of money to get the present value of $100 using different periods of time and interest rates.
TimeValue ofMoney
In the world of business, it is essential to know what TVM represents and how it helps make better choices in how we spend our money. TVM is also known as TimeValue of money which is a given amount of interest earned in a period of time (Wikipedia, 2011). Each member in group “C” will use 100 as our present value and we will choose an interest rate and period. Timevalue of money concept is used to determine present and future values of money. “The timevalue of money refers to the relationship between time, money, and the rate of interest.” (Letsche, 2011). The formula consist of four components FV = Future Value, PV = Present Value, i = the interestrate per period and n= the number of compounding periods (TeachMeFinance.com)....

...Introduction
The timevalue of money is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. The timevalue of money can be defined as the value of money received today instead of in the future. This is based on the premise that cash in hand today is more valuable than the same amount in the future due to its capability of earning interest. For investors, this is single most important concept in the world of finance. This paper will discuss the different financial applications of the timevalue of money. This paper will also describe the components of interest and highlight various methods of calculating timevalue of money using different interest scenarios.
Financial Applications of the TimeValue of MoneyTimevalue of money has many useful applications. One of the most important uses is that it helps to measure the trade-off in spending and saving. This can have important consequences for your personal budgeting. If market interest rates are at 5%, one may decide that the timevalue of money is greater in the future, and...

...Abstract
The first steps toward understanding the relationship between the value of dollars today and that of dollars in the future is by looking at how funds invested will grow over time. This understanding will allow one to answer such questions as; how much should be invested today to produce a specified future sum of money?
TimeValue of Money
In most cases, borrowing money is not free, unless it is a fiver for lunch from a friend. Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per a period of time, usually one year. The current market rates are composed of three items.
The Real Rate of Interest is what compensates lenders for postponing their own spending during the term of the loan. An Inflation Premium is added to offset the possibility that inflation may eat into the value of the money during the term of the loan. In addition, various Risk Premiums are added to compensate the lender for risky loans such as unsecured loans made to borrowers with questionable credit ratings or loans that the lender may not be able to easily resell.
The first two components of the interest rate listed above, the real rate of interest and an inflation premium, together are referred to as the nominal risk-free rate. In the United States, the nominal risk-free...

...In financial management, one of the most important concepts is the TimeValue of Money (TVM). TimeValue of Money concepts helps a manager or investors understand the benefits and the future cash flow to help justify the initial cost of the project or investment. Many of the assets businesses and individuals own are financed with money borrowed from others, so the understanding of TVM is crucial to making good buying decisions. To recognize how annuities affect the timevalue of money, managers need to consider the factors of interest rate, opportunity costs, future and present values of money, and compounding.
Interest Rates and CompoundingIn most business cases, borrowing money is not necessarily a free enterprise. It costs companies money to obtain funds on credit to finance various aspects of their business. The fee that a borrower pays to a lender for use of its money is interest. The annual percentage rate (APR) makes assumptions based on simple interest, which is interest only earned on the principal investment.
Another method of accruing interest is through compounding. Compound interest is not only charged on the original investment, but also assessed on the interest charged or earned for each period. "When comparing interest rates, it is best to use...

...flow payments is a set of:
a. level cash flows occurring each time period for a fixed length of time.
b. level cash flows occurring each time period forever.
c. increasing cash flows occurring each time period for a fixed length of time.
d. increasing cash flows occurring each time period forever.
e. arbitrary cash flows occurring each time period for no more than 10 years.
c 4. An annuity stream where the payments occur forever is called a(n):
a. annuity due.
b. indemnity.
c. perpetuity.
d. amortized cash flow stream.
e. amortization table.
c 5. The interest rate expressed as if it were compounded once per year is called the _____ rate.
a. stated interest
b. compound interest
c. effective annual
d. periodic interest
e. daily interest
b 6. The interest rate charged per period multiplied by the number of periods per year is called the _____ rate.
a. effective annual
b. annual percentage
c. periodic interest
d. compound interest
e. daily interest
b 7. You are comparing two investment options. The cost to invest in either option is the
same today. Both options will provide you with $20,000 of income. Option A pays five
annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of the
following statements is correct given these two investment...

...that Lancer leasing company requires a 9% rate of return, what is the PV of payments?
PV = $120,663
4. The Mutual Assurance and life Company is offering an insurance policy under either of the following two terms:
a) Make a series of 12 payments of $1,200 at the beginning of each of the next 12 years (first payment being made today)
b) Make a single lump-sum payment today of 10,000 and receive coverage for the next 12 years
If you had investment opportunities offering an 8% annual return, which alternative would you prefer?
a) PV = $9,766.66
b) PV = $10,000
Select option a
5. A leading broker has advertised money multiplier certificates that will triple your money in 9 years; that is if you buy one for $333.33 today, it will pay you $1,000 at the end of 9 years? What rate of return will you earn on this money multiplier certificates?
i = 13.073%
6. Given two following mutually exclusive alternatives:
a) Alternative A: initial cost $100, annual benefits $60, useful life 7 years
b) Alternative B: initial cost $60, annual benefits $20, useful life 7 years
Which alternative is preferable if i = 12%?
a) PV = $173.84
b) PV = $31.28
Select option a
7. Project A and B have first costs of $10,000 and $18,000, respectively. Project A has net annual benefits of $5,000 during each year of its 5 year useful life, after which it can be replaced...

...TimeValue of Money
Exercise
1. If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now, assuming no withdrawals in interim?
2. a. If you invest $100 every year from the next 20 years starting one year from today and you earn interest of 10% per year, how much will you have at the end of the 20 years?
b. How much must you invest each year if you want to have $50000 at the end of the 20 years?
3. What is the present value of the following cash flows at an interest rate of 10% per year? (Hints: don’t need to use the financial keys of your calculator, just dome common sense)
a. $100 received five years from now
b. $100 received 60 years from now
c. $100 received each year beginning one year from now and ending 10 years from now
d. $100 each year beginning one year from now and continuing forever
4. You want to establish a “wasting” fund, which will provide your with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year?
5. You take a one-year installment loan of $1000 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments.
a. What is the monthly payment?
b. What is the total amount of interest paid over the 12-month term of the loan?
6. You are taking out a $100000 mortgage...

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