A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 12 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity?
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A 15-year annuity pays $1,500 per month, and payments
are made at the end of each month. If the interest rate is 12 percent compounded
monthly for the first seven years, and 6 percent compounded monthly thereafter,
what is the present value of the annuity?
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- In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, 20; year 2, 82; year 3, 60; year 4, 2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)A 5-year annuity of ten $5,300 semiannual paymentswill begin 9 years from now, with the first payment coming 9.5 years from now. If thediscount rate is 12 percent compounded monthly, what is the value of this annuityfive years from now? What is the value three years from now? What is the currentvalue of the annuity?
- You are managing a portfolio of $1 million. Your target duration is 11 years, and you can choose from two assets: a zero coupon bond with maturity 5 years, and a perpetuity, the yield is: A. .688 B. .417 C. .583 D. .312A few years ago, Michael purchased a home for $394,000. Today, the home is worth $520,000. His remaining mortgage balance is $166,000. Assuming Michael can borrow up to 80 percent of the market value of his home, what is the maximum amount he can borrow?You are saving for the college education of your two children. They aretwo years apart in age; one will begin college 15 years from today and the otherwill begin 17 years from today. You estimate your children’s college expenses to be$45,000 per year per child, payable at the beginning of each school year. The annualinterest rate is 7.5 percent. How much money must you deposit in an account eachyear to fund your children’s education? Your deposits begin one year from today.You will make your last deposit when your oldest child enters college. Assume fouryears of college.
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