There are multiple questions that I need help answering:
1. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 6.6%. Now, with 6 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 13%. What is the price of the bond now? (Assume semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price = $_______
2. Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 86% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Yield to maturity = _____%
3. If you earn 7% per year on your bank account, how long will it take an account with $115 to double to $230? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Number of years _____
4. An engineer in 1950 was earning $5,000 a year. Today she earns $50,000 a year. However, on average, goods today cost 7.8 times what they did in 1950. What is her real income today in terms of constant 1950 dollars? (Round your answer to 2 decimal places.) Today's real income $
5. In April 2013 a pound of apples cost $1.46, while oranges cost $1.10. Two years earlier the price of apples was only $1.25 a pound and that of oranges was $.96 a pound.
a. What was the annual compound rate of growth in the price of apples? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Compound annual growth rate % per year
b. What was the annual compound rate of growth in the price of oranges? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Compound annual growth rate % per year
c. If the same rates of growth persist in the future, what will be the price of apples in 2030? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price $
d. If the same rates of growth persist in the future, what will be the price of oranges in 2030? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price $
6. How much will $100 grow to if invested at a continuously compounded interest rate of 11.75% for 9 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Future value $
b. What if it is invested for 11.75 years at 9%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Future value $
7. A store will give you a 3.50% discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Effective annual rate %
8. A couple will retire in 50 years; they plan to spend about $36,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings.
a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual payment $
b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $66,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual payment $
9. Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $160,000 and 2 points are charged, the loan repayment schedule is calculated on a $160,000 loan but the net amount the borrower receives is only $156,800. Assume the interest rate is 1.00% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 288 months? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Use a financial calculator or Excel.) Effective annual interest rate %
10. You take out a 20-year $290,000 mortgage loan with an APR of 9% and monthly payments. In 11 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? (Round the monthly loan payment to 2 decimal places when computing the answer. Round your answer to 2 decimal places.) Principal balance on the loan $
11. A local bank advertises the following deal: Pay us $100 at the end of each year for 11 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever.
a. Calculate the present value of your payments to the bank if the interest rate available on other deposits is 6.25%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value $
b. What is the present value of a $100 perpetuity deferred for 11 years if the interest rate available on other deposits is 6.25%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value $
c. Is this a good deal? Yes or No
12. A famous quarterback just signed a $14.0 million contract providing $2.6 million a year for 4 years. A less famous receiver signed a $13.0 million 4-year contract providing $3 million now and $2.5 million a year for 4 years. The interest rate is 8%.
a. What is the PV of the quarterback's contract? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) Present value $ million
b. What is the PV of the receiver's contract? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) Present value $ million c. Who is better paid? Quarterback Receiver
13. Find the interest rate implied by the following combinations of present and future values: (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places) Present Value Years Future Value Interest Rate $ 420 10 $ 826 % 193 3 257 % 320 6 320 %
14. You can buy property today for $3.3 million and sell it in 5 years for $4.3 million. (You earn no rental income on the property.)
a. If the interest rate is 9%, what is the present value of the sales price? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.) Present value $ million
b. Is the property investment attractive to you? Yes No c-1. What is the present value of the future cash flows, if you also could earn $230,000 per year rent on the property? The rent is paid at the end of each year. (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.) Present value $ million c-2. Is the property investment attractive to you now? Yes or No
15. In 1880 five aboriginal trackers were each promised the equivalent of 50 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1997 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $50. However, the granddaughters also claimed that they were entitled to compound interest.
a. How much was each granddaughter entitled to if the interest rate was 4%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Future value A$
b. How much was each entitled to if the interest rate was 8%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Future value A$
16. Compute the future value of a $150 cash flow for the following combinations of rates and times. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Future Value a. r = 7%, t = 10 years $ b. r = 7%, t = 20 years $ c. r = 3%, t = 10 years $ d. r = 3%, t = 20 years $