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- The present value of y dollars after x years at 15% continu- ous interest is f(x, y) = ye¬0.15x. Sketch some sample level curves. (Economists call this collection of level curves a dis- count system.)A state lottery gives a winner the choice of receiving the winning amount in equal monthly payments for 20 years or receiving a lump sum equal to the present value of an annuity with future value equal to the winnings. The winner selecting monthly payments will receive $4,000,000/240 = $16,666.67 each month for each million dollars of winnings. (Round your final answers to two decimal places.) (a) Find the present value of an annuity with monthly payments of $16,666.67, at an Interest rate of 5.2% for 20 years, for the winner who wants a lump-sum payment. $ X (b) In order for the lottery to be more profitable, it is decided to pay the winnings in equal monthly payments for 25 years. Find the monthly payments of $4 million in winnings. $ Find the present value of an annuity with those monthly payments at 5.2% for 25 years. $What does this chart say about the 1%?
- is based on the notion that a dollar paid in the future is less valuable than a dollar paid today. The present value of a loan in which $1000 is to be paid out a year from today with the interest rate equal to 1% is $. (Round your response to the neareast two decimal place) If a loan is paid after two years, and the amount $1000 is to be paid then with a corresponding 2% interest rate, the present value of the loan is $. (Round your response to the neareast two decimal place) Next 11:41 AM1. How much is the total value of all these presents worth today?2. How much is the future value of all these presents at the end of 12 years?3. If Tita Rhea agrees to give her these amounts annually forever, how much is its total value worth today?4. If the presents are each made continuously throughout the year at a rate of P, multiply the present value in #7 by a suitable adjustment factor (d/δ) to determine its total present value. Type the resulting amount below.A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $3,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 4% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 15% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? ARCKICHI a. What is today's value of the bequest? Today's value of the bequest is $(Round to the nearest dollar. b. What is the value of the bequest immediately after the first payment is made? The value of the bequest immediately after the first payment is made is $ (Round to the nearest dollar.)
- 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.Suppose a person has a total credit card debt of $1,500$1,500 that has a 7%7% yearly interest rate. This person also has a savings account with $2,500$2,500 that pays 2%2% interest per year. Despite the net loss, the person keeps both.Calculate how many times the person appreciates the $1$1 of savings more than $1$1 of credit card debt if the person relates similarly to both values of percent paid and received. Enter your answer in the box below and round to two decimal places if necessary.Present value is the value in today's dollars of funds to be paid or recelived in the future. If the current interest rate is 8%, then the present value of $1,000 to be received in7 years is $ (Enter your response rounded to two decimal places.)
- How much money must you invest today in order to grow to a value of $45,000 in 10 years if your money grows at 5%? Your Answer: AnswerThe value of land in Manhattan was around $150 billion in 2008. Imagine that it is 1626 and you are the economic advisor to the Dutch when they are considering whether to buy Manhattan from the Manhasset Indians. Further,assume that the relevant interest rate for calculating the present value is 4%per year. Would you advice the Dutch that a purchase price of $24 is a good deal or not? How would your answer change if the interest rate were 6%? And 8%? (Hint: for each interest rate,calculate the present value in 1626 of the land value as of 2008. Then compare that with the purchase price in 1626. For example, simplify by assuming that the owners collect no rents on the land. As an advanced further question,assume that the rent equals 2% of the value of the land each year.)5 Question Let Ya,n be the present value of an n-year term continuous annuity of $1 per year for an insured aged x. Let Y be the present value of a whole life continuous annuity of $1 per year for an insured aged x. Given a constant force of interest, 8, show that: 1 бп Cov (Yz,n, Yz) = (A — e¯ðª‚„Ez (1 − Āz+n) — ±‚ñ¦Ã‚) 82 n. - -