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...
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