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Chapter 15: Problem 1

Suppose the interest rate is 10 percent. If \(\$ 100\) is in vested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of \(\$ 100\) paid one year from now? Paid two years from now? Paid five years from now?

Short Answer

Expert verified
Placement of $100 today will be worth $110 after one year, $121 after two years, and $161.05 after five years. The current value of $100 that is to be paid in the future is $90.91 one year from now, $82.64 two years from now, and $62.09 five years from now.

Step by step solution

01

Find the future worth of $100 after one, two and five years respectively

Use the simple interest formula with P as $100, r as 10% (or 0.10), n as 1 (since it is compounded annually), and t as the respective years for each case. So, after one year, the amount \( A = 100 * (1 + 0.10/1)^1 = \$110 \). Similarly, after two years \( A = 100 * (1 + 0.10/1)^2 = \$121 \) and after five years \( A = 100 * (1 + 0.10/1)^5 = \$161.05 \)
02

Find the present value of $100 paid after one, two and five years

Using the Present Value formula, \( PV = FV / (1 + r)^t \), calculate the present value for each of the specified years. For a payment after one year, the present value is \( PV = 100 / (1 + 0.10)^1 = \$90.91 \). Similarly, for two years \( PV = 100 / (1 + 0.10)^2 = \$82.64 \) and for five years \( PV = 100 / (1 + 0.10)^5 = \$62.09 \)

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Most popular questions from this chapter

A bond has two years to mature. It makes a coupon payment of \(\$ 100\) after one year and both a coupon payment of \(\$ 100\) and a principal repayment of \(\$ 1000\) after two years. The bond is selling for \(\$ 966 .\) What is its effective yield?

Suppose the interest rate is 10 percent. What is the value of a coupon bond that pays \(\$ 80\) per year for each of the next five years and then makes a principal repayment of \(\$ 1000\) in the sixth year? Repeat for an interest rate of 15 percent.

A consumer faces the following decision: She can buy a computer for \(\$ 1000\) and \(\$ 10\) per month for Internet access for three years, or she can receive a \(\$ 400\) rebate on the computer (so that its cost is \(\$ 600\) ) but agree to pay \(\$ 25\) per month for three years for Internet access. For simplification, assume that the consumer pays the access fees yearly (i.e., \(\$ 10\) per month \(=\$ 120\) per year) a. What should the consumer do if the interest rate is 3 percent? b. What if the interest rate is 17 percent? c. At what interest rate will the consumer be indifferent between the two options?

The market interest rate is 5 percent and is expected to stay at that level. Consumers can borrow and lend all they want at this rate. Explain your choice in each of the following situations: a. Would you prefer a \(\$ 500\) gift today or a \(\$ 540\) gift next year? b. Would you prefer a \(\$ 100\) gift now or a \(\$ 500\) loan without interest for four years? c. Would you prefer a \(\$ 350\) rebate on an \(\$ 8000\) car or one year of financing for the full price of the car at 0-percent interest? d. You have just won a million-dollar lottery and will receive \(\$ 50,000\) a year for the next 20 years. How much is this worth to you today? e. You win the "honest million" jackpot. You can have \(\$ 1\) million today or \(\$ 60,000\) per year for eternity right that can be passed on to your heirs). Which do you prefer? f. In the past, adult children had to pay taxes on gifts of over \(\$ 10,000\) from their parents, but parents could make interest-free loans to their children. Why did some people call this policy unfair? To whom were the rules unfair?

Suppose you can buy a new Toyota Corolla for \(\$ 20,000\) and sell it for \(\$ 12,000\) after six years. Alternatively, you can lease the car for \(\$ 300\) per month for three years and return it at the end of the three years. For simplification, assume that lease payments are made yearly instead of monthly-i.e., that they are \(\$ 3600\) per year for each of three years. a. If the interest rate, \(r,\) is 4 percent, is it better to lease or buy the car? b. Which is better if the interest rate is 12 percent? c. At what interest rate would you be indifferent between buying and leasing the car?
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