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Suppose you invest $3,000 today and have the following alternative depositing options:
- The annual interest rate of 9.00% compounded quarterly;
- The annual interest rate of 8.25% compounded monthly;
- The annual interest rate of 7.95% compounded daily;
Which of the above mentioned options is best for you and why?
Step by step
Solved in 3 steps
- Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $4,200 over the next 6 years when the interest rate is 8%, how much do you need to deposit in the account? B. If you place $8,700 in a savings account, how much will you have at the end of 12 years with an interest rate of 8%? C. You invest $2,000 per year, at the end of the year, for 20 years at 10% interest. How much will you have at the end of 20 years? D. You win the lottery and can either receive $500,000 as a lump sum or $60,000 per year for 20 years. Assuming you can earn 3% interest, which do you recommend and why?Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $2,500 over the next 4 years when the interest rate is 15%, how much do you need to deposit in the account? B. If you place $6,200 in a savings account, how much will you have at the end of 7 years with a 12% interest rate? C. You invest $8,000 per year for 10 years at 12% interest, how much will you have at the end of 10 years? D. You win the lottery and can either receive $750,000 as a lump sum or $50,000 per year for 20 years. Assuming you can earn 8% interest, which do you recommend and why?
- You put $250 in the bank for S years at 12%. A. If interest is added at the end of the year, how much will you have in the bank after one year? Calculate the amount you will have in the bank at the end of year two and continue to calculate all the way to the end of the fifth year. B. Use the future value of $1 table in Appendix B and verity that your answer is correct.(1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? (2) What is the PV of the same stream? (3) Is the stream an annuity? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when INOM = EFF% = IPER.) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM/2 = 10%/2 = 5%?Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semi-annually. If you make 20 consecutive semi-annual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20? Group of answer choices $52,821.19 $57,900.83 $58,988.19 $62,527.47 $64,131.50
- If an investor wants to earn an annual interest rate of 10.76% on a 26 week T-bill with a maturity value of $5,000, how much should the investor pay for the bill?You investe an amount of P50,000 with a promised interest of 9% compounded quarterly. How many years will it take for the money to become twice the original amount? What is the effective interest rate? Taking into consideration the inflation rate which is 6%, what is the actual purchasing power of your investment by the time you choose to withdraw it?You intend to save for retirement over the upcoming 30 years by allocating R850 monthly to a stock account and R250 monthly to a bond account. The expected return for the stock account is 11%, while the bond account is anticipated to yield 6%. Upon retirement, you plan to merge your funds into an account with a 5% return. All interest rates are Annual Percentage Rates (APRs) compounded monthly. What would be the monthly withdrawal amount from your account over a 25-year period post - retirement?
- You are planning to save for retirement over the next 35 years. To do this, you will invest $770 per month in a stock account and $370 per month in a bond account. The return of the stock account is expected to be 9.7 percent, and the bond account with pay 5.7 percent. When you retire, you will combine your money into an account with a 6.7 percent return. How much can you withdraw each month from your account assuming a 30-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16)You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in an account A and $300 a month in an account B. The return of the stock account is expected to be 11 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a 9 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?Suppose that you have opened a saving account with an initial deposit of $10,000. The account offers an annual interest rate of 2.5% compounded quarterly. (c) What should be the annual interest rate so that the worth value of the investment reaches $15,000 in only 10 years?
