2024 – Compounding frequency and time value You plan to invest 2 000 in an individual retirement

 Compounding frequency and time value You plan to invest $2,000 in an individual

retirement arrangement (IRA) today at a nominal annual rate of 8%, 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

(1) annually, (2) semiannually, (3) daily (assume a 365-day year), and (4) continuously?

 

b. What is the effective annual rate, EAR, for each compounding period in part a?

c. How much greater will your IRA 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 through c

 

Value of a single amount versus a mixed stream Gina Vitale has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay $24,000 at the closing of the transaction or will pay the amounts shown in the following table at the beginning of each of the next 5 years. Because Gina doesn’t really need the money today, she plans to let it accumulate in an account that earns 7% annual interest. Given her desire to buy a house at the end of 5 years after closing on the sale of the lot, she decides to choose the payment alternative

 

$24,000 single amount or the mixed stream of payments in the following table that provides the higher future value at the end of 5 years. Which alternative will she choose?

 

Retirement planning Hal Thomas, a 25-year-old college graduate, wishes to retire at age 65. To supplement other sources of retirement income, he can deposit $2,000 each year into a tax-deferred individual retirement arrangement (IRA). The IRA will earn a 10% return over the next 40 years

 

 Time value An Iowa state savings bond can be converted to $100 at maturity 6 years from purchase. If the state bonds are to be competitive with U.S. savings bonds, which pay 8% annual interest (compounded annually), at what price must the state sell its bonds? Assume no cash payments on savings bonds prior to redemption.

 

Time value As part of your financial planning, you wish to purchase a new car

exactly 5 years from today. The car you wish to purchase costs $14,000 today, and

your research indicates that its price will increase by 2% to 4% per year over the next 5 years.

 

a. Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.

 

b. How much more expensive will the car be if the rate of inflation is 4% rather than 2%?

 

c. Estimate the price of the car if inflation is 2% for the next 2 years and 4% for 3 years after that

 

 Future value calculation Without referring to the preprogrammed function on your financial calculator, use the basic formula for future value along with the given interest rate, r, and the number of periods, n, to calculate the future value of $1 in

 

 

each of the cases shown in the following table.