Time Value of Money: Example
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1.) You need $25,000 today and have decided to take out a loan at 7 percent for five years. Which one of the following loans would be the least expensive? Assume all loans require monthly payments and that interest is compounded on a monthly basis.
2.) You grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return?
3.) A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 8 percent?
4.)The Pawn Shop loans money at an annual rate of 21 percent and compounds interest weekly. What is the actual rate being charged on these loans?
5.) The preferred stock of Casco has a 5.48 percent dividend yield. The stock is currently priced at $59.30 per share. What is the amount of the annual dividend?
6.) Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17?
7.) You borrow $165,000 to buy a house. The mortgage rate is 7.5 percent and the loan period is 30 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay?
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This solution provides assistance determining the time value of money.
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