5. Suppose that as a lottery prize you win a trip worth $8,000. You are uninterested in the trip, but under the terms of the prize you can collect the $8,000 in cash, but only if you do not redeem the prize for 3 years. If the interest rate is 5%, the present value of the prize is a) $6911 b) $7619 c) $8,000 d) $21,786
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- Investors sometimes fear that a high-risk investment is especially likely to have low returns. Is this fear true? Does a high risk mean the return must be low?Economics In 54 months time you expect a cash flow of $3 million. Calculate it’s present value (PV) given the 54-month interest rate is currently 4%, with a volatility of 120 basis points (bps). Explain, using equations with properly-defined mathematical notation, how to map this cash flow to vertices at 4 years and 5 years, in such a way that the volatility of the present value of the mapped cash flow remains at 120 bps. Suppose the 4-year rate has a volatility of 110 bps and the 5-year rate has a volatility of 150 bps, and their correlation is 0.9. How much should be mapped to each vertex. Give your answer in PV terms and round your answers to whole $ values.a) Suppose you put $350 into a bank account today. Interest is paid annually and the annual interest rate is 6 percent. What is the future value of the $350 after 4 years? b) Suppose you are deciding whether to buy a particular bond from your local municipality. If you buy the bond and hold it for 4 years, then at that time you will receive a payment of $10,000. Assume the interest rateis6percent. Underwhatcircumstanceswillyoubuythebond?Meaninguptowhatpriceareyou willing to pay.
- 2. Assume a bond with the following characteristics: face value = $1000; maturity = 5 years; N yearly coupon payments = $100. a. If the current price of this bond is $850, state what the formula is to calculate the bond's yield to maturity and state the range of interest rates where the yield to maturity should fall b. If you purchased this bond at face value and held it for 1 year, when you resold it for $850, what is the bond's rate of return?Problem 2 Suppose you purchased a house and took a 30 -year mortgage. The mortgage is unusual: you pay yearly, not monthly. The yearly payment is$17,000and the interest rate is4.2%. What is the amount of mortgage you took? (Round to two decimals.) Hint: find the PV of all the payments.6. An investor purchases a 30-year U.S. government bond for $840. The bond’s couponrate is 10 percent and, it still had twelve years remaining until maturity. If the investorholds the bond until it matures and collects the $1000 par value from the Treasuryand his marginal tax rate is 25 percent (we assume that the bond is taxable), what willbe his after-tax (effective) yield to maturity? Make sure to show your work.
- Suppose that you purchase a 2 year coupon bond at the time it is issued for $1100. The face value of the bond is $1000, with annual coupon payments of $80. a. What is the bond’s “coupon rate”? b. What is the bond’s “current yield”? c. What is the bond’s (nominal) “yield to maturity”? d. If you hold the bond for 1 year and sell it for $1035 (after collecting the first coupon payment), what is your “holding period rate of return”? Please answer all part otherwise Dounvote1. A present obligation of $20,000 is to be repaid in equal uniform annual amounts, each of which includes repayment of the debt (principal) and interest on the debt, over a period of 5 years. If the interest per year is 10%, what is the amount of the annual repayment? 2. Suppose that the $20,000 above is to be paid at a rate of $4,000 per year plus the interest that is owed and based on the beginning of year unpaid principal. Compute the total amount of interest repaid in this situation and compare it with that of the problem above. Why are the 2 amounts different? Solve all questions compulsory....Annuity 1. If a certain machine undergoes a major overhaul now, its output can be increased by 20% - which translates into additional cash flow of $20,000 at the end of each year for five years. If i = 15% per year, how much can we afford to invest to overhaul this machine? 2. You are running a bank. A customer agrees to pay you $100,000 each year with annual interest rate of 10% for 5 years. How much money will you lend to him?
- Property taxes in a particular district are 2% of thepurchase price of a home every year. If you just purchased a $150,000 home, what is the present value ofall the future property tax payments? Assume that thehouse remains worth $150,000 forever, property taxrates never change, and a 4% interest rate is used fordiscounting10. Suppose the interest rate is 5% and that you are to receive three annual payments of $10,000, with the first payment one year from now, the second payment two years from now, and the third payment three years from now. What is the present value of this stream of payments?4. Joyce buys a television set from a merchant who asks P 18,750 at the end of 60 days (cash in 60 days). Joyce wishes to pay immediately and the merchant offers to compute the cash price on the assumption that money is worth 8% simple interest. What is the cash price today?