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...

...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 of Money
In the world of business, it is essential...

...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...

...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...

...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...

...9.99 percent
a 3. An annuity stream of cash 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...

...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:...

...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?...

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