going to earn ωt = $200,000 when working (age 21 and 60), and then you are going to live for the next 20 years with ωt = $0. Find the constant level of consumption C during years (21-80) that can be financed by your income (Interest rate is 5%). Find the level of savings St = ωt −C for periods t ≤60 and for t > 60
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You are going to earn ωt = $200,000 when working (age 21 and 60), and then
you are going to live for the next 20 years with ωt = $0. Find the constant level of
consumption C during years (21-80) that can be financed by your income (Interest
rate is 5%). Find the level of savings St = ωt −C for periods t ≤60 and for t > 60
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- Multiperiod Consumption-Saving Plan Assume a person is 35 years old and plans to retire at age 65. So s/he has 30 more years to work. Assume the following additional information apply: Annual (real) income = $40,000 Real interest rate = 5% Expected live after retirement = 20 years Desired retirement income = 75% of pre-retirement income = $30,000 Prepare lifetime consumption-savings schedule for the person. First calculate how much s/he should have at retirement in order to consume $30,000 per year for 20 more years. This is the PV of annuity of $30,000 over 20 years at interest rate of 5%. 30,000* (PVIFAs°20) = $373,866.31. This amount is also equal to the future value of what s/he should save over her/his remaining 30 working years. (Annual saving)* (FVIFAS9,30) = $373,866.31. Solve for annual saving and you will get $5,627.22.Assume that your father is now 50 years old and plans to retire after 10 years from now. He is expected to live for another 25 years after retirement. He wants a fixed retirement income of Rs. 5,00,000 per annum. His retirement income will begin the day he retires, 10 years from today, and then he will get 24 additional payments annually. Your father has current savings of Rs. 10,00,000 and he expects to earn a return on his savings @ 10% p.a., annually compounding. How much (to the nearest of rupee) must your father save during each of next 10 years to meet his retirement goal?What is the definition of internal rate of return (IRR)? If you expect the annual interest rates are much different in the next 10 years, would the IRR be the ideal measure? Why or why not?
- A company is considering a new manufacturing process. It knows that the rate of savings (in dollars per year) from the process will be about S(t)-3000(1+4) where t is the number of years the process has been in use. Find the total savings during the first year Find the total savings during the first 7 years The total savings during the first year is (Simplify your answer.)You inherit $10K when you are 20. What is this worth when you are ready to retire at 65? Assume that the money can be invested at 7%, which is your interest rate for the time value of money. Compare this with an insurance policy that could be purchased with a lump-sum payment of $10K. That policy would pay you $100K at age 65 and your survivors $100K if you die sooner. How much value per year must you put on protecting your survivors for these to be equivalent?Suppose that $500 is invested at the end of every year for 5 years. The polynomial function that models the value of the investment is P(x) = 500x5 + 500x4 + 500x³ + 500x² + 500x, where x represents the effective interest rate plus 100%. One year after the last payment, the investment is worth $3200. Find the effective interest rate one year after the last payment, to the nearest tenth. (Note: You will need to subtract 1 from the value of x to find the effective interest rate.)
- You are planning to become a millionaire (i.e., save $1 M) over the next 30 years when you finally retire. a) If you are earning interest at the rate of 5% and you live 15 years after retirement, what annual level of living expenses can you afford with your savings? b) Suppose your retirement living expenses will increase at an annual rate of 3% due to inflation. Determine the annual spending plan in line with your inflationAn investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What i are the nominal, periodic, and effective interest rates for this investment opportunity? Interest Rates Nominal rate Periodic rate Effective annual rate Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding bimonthly (every two months). What is the effective interest rate that Rahul would pay for the loan? ○ 3.945% 4.152% 4.067% 04.186 % Another bank is also offering favorable terms, so Rahul decides to take a loan of $12,000 from this bank. He signs the loan contract at 5% comanded daily for 12 months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days,…The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). (Round the final answers to 2 decimal places.) a. Suppose that today you buy an 9.2% annual coupon bond for $1,180. The bond has 19 years to maturity. What rate of return do you expect to earn on your investment? Expected rate of return % b-1. Two years from now, the YTM on your bond has declined by 1%, and you decide to sell. What price will your bond sell for? (Omit $ sign in your response.) Bond price $ b-2. What is the HPY on your investment? HPY %
- A consumer's income in the current period is y = 100 and income in the future period is y'= 120. He or she pays lump-sum taxes t=20 in the current period and t'= 10 in the future period. The real interest rate is 0.1, or 10%, per period. (a) Determine what the consumer's optimal current-period and future-period consump tions are, and what optimal saving is, and show this in a diagram with the consumer's budget constraint and indifference curves. Is the consumer a lender or a borrower? (b) Now suppose that instead of y = 100 the consumer has y = 140 Again, determine optimal consumption in the current and future periods and optimal saving, and show this in a dia gram. Is the consumer a lender or a borrower? (c) Explain the differences in your results be tween parts (a) and (b).Lorenz curves also can be used to provide a relative measure of the distribution of the total assets of a country. Using data in a report by the economic committee of a certain country, an economist produced the following Lorenz curves for the distribution of total assets in the country in 1963 and 1983, shown below. f(x) = x10 Lorenz curve for 1963 g(x) = x13 Lorenz curve for 1983 Find the Gini index of income concentration for each Lorenz curve and interpret the results. .... What is the Gini index for 1963? (Round to three decimal places as needed.) What is the Gini index for 1983? (Round to three decimal places as needed.) Interpret your results. O A. Total assets were more equally distributed in 1963 O B. Total assets were more equally distributed in 1983 O c. Total assets were distributed the same in 1963 as in 1983.Determine the present value P you must invest to have the future value A at simple interest rate r after time t. A = $6000.00, r = 9.0%, t = 26 weeks (Round to the nearest cent.)