A recent television commercial made the statement that if a person invests $750 at the beginning of each month for 35 years, they could have $1,000,000 for retirement. Assuming monthly compounding, what annual interest rate is implied in this statement?
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- Say that you plan to retire one quarter after making quarterly contributions to a retirement account for 10 years. You plan to make quarterly contributions of $1007 to an investment account that will earn 10.0% interest annually. If your first contribution occurs today, then what is the account balance when you retire? (Round to the nearest dollar)Suppose that you'd like to retire in 40 years and you want to have a future value of $ 500000 in a savings account. Also suppose that your employer makes regular monthly payments into your retirement account. If you can expect an APR of 7.5% for your account, how much do you need your employer to deposit each month? Employer Contribution = The formulas we have been using assume that the interest rate is constant over the period in question. Over a period of 40 years, though, interest rates can vary widely. To see what difference the interest rate can make, let's assume a constant APR of 4% for your retirement account. How much do you need your employer to deposit each month under this assumption? Employer Contribution = rate dic resta. You plan to invest $5,000 in an individual retirement arrangement today at a nominal annual interest rate of 10%, which is expected to apply to all future years. 1. How much you will have in the account at the end of 15 years if interest is compounded (1) annually? (2) Semiannually? (3) Quarterly and (4) daily (assume a 365-day a year)? 2. Compute effective annual rate and explain the relationship exists between compounding frequency and the nominal and effective annual rates ?
- You have decided you would like to deposit $5,000 into your account today and not touch it until you retire in 45 years. You would like to have accumulated $80,000 at retirement from this deposit if your savings account pays interest quarterly. a)What would your nominal required rate of return (% per annum) be on this deposit? b)What would your effective annual rate of return be on this deposit?Suppose that you'd like to retire in 40 years and you want to have a future value of $ 800000 in a savings account. Also suppose that your employer makes regular monthly payments into your retirement account. If you can expect an APR of 7.5% for your account, how much do you need your employer to deposit each month? Employer Contribution = The formulas we have been using assume that the interest rate is constant over the period in question. Over a period of 40 years, though, interest rates can vary widely. To see what difference the interest rate can make, let's assume a constant APR of 4% for your retirement account. How much do you need your employer to deposit each month under this assumption? Employer Contribution =As part of your retirement plan, you have decided to deposit $9,000 at the beginning of each year into an account paying 3% interest compounded annually. (Round your answers to the nearest cent.) (a) How much (in $) would the account be worth after 10 years? $ (b) How much (in $) would the account be worth after 20 years? $ (c) When you retire in 30 years, what will be the total worth (in $) of the account? $ (d) If you found a bank that paid 6% interest compounded annually rather than 3%, how much (in $) would you have in the account after 30 years? $ (e) Use the future value of an annuity due formula to calculate how much (in $) you would have in the account after 30 years if the bank in part (d) switched from annual compounding to monthly compounding and you deposited $750 at the beginning of each month instead of $9,000 at the beginning of each year. $ Submit Ancworl
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a stated interest rate of 8 percent, which is expected to apply to all future years.a. How much will you have in the account at the end of 10 years if interest is compounded as follows?(1) Annually(2) Semiannually(3) Daily (assume a 360-day year)(4) Continuouslyb. What is the effective annual rate (EAR) for each compounding period in part a?c. How much greater will your IRA account balance be at the end of 10 years if interest is compounded continuously rather than annually?d. How does the compounding frequency affect the future value and effective annual rate for a given deposit? Explain in terms of your findings in parts a–c.As part of your retirement plan, you have decided to deposit $9,000 at the beginning of each year into an account paying 5% interest compounded annually. (Round your answers to the nearest cent.) Explain A-E (a) How much (in $) would the account be worth after 10 years? $ (b) How much (in $) would the account be worth after 20 years? $ (c) When you retire in 30 years, what will be the total worth (in $) of the account? $ (d) If you found a bank that paid 6% interest compounded annually rather than 5%, how much (in $) would you have in the account after 30 years? $ (e) Use the future value of an annuity due formula to calculate how much (in $) you would have in the account after 30 years if the bank in part (d) switched from annual compounding to monthly compounding and you deposited $750 at the beginning of each month instead of $9,000 at the beginning of each year. $Suppose a man retires at age 65, and in addition to Social Security, he needs $2200 per month in income. Based on an expected lifetime of 204 more months, how much would he have to invest in a life income annuity earning 4% APR to pay that much per year? (Round your answer to two decimal places.)