calculate the future value

calculate the future value

Future value calculation Without referring
Subject: Business    / Finance   
Question

P5–2 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.

Case Interest rate, r Number of periods, n
A 12% 2
B 6 3
C 9 2
D 3 4


P5–6 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.


P5–14 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.


P5–22 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.
a. If Hal makes annual end-of-year $2,000 deposits into the IRA, how much will he
have accumulated by the end of his sixty-fifth year?
b. If Hal decides to wait until age 35 to begin making annual end-of-year $2,000
deposits into the IRA, how much will he have accumulated by the end of his
sixty-fifth year?
c. Using your findings in parts a and b, discuss the impact of delaying making deposits
into the IRA for 10 years (age 25 to age 35) on the amount accumulated
by the end of Hal’s sixty-fifth year.
d. Rework parts a, b, and c, assuming that Hal makes all deposits at the beginning,
rather than the end, of each year. Discuss the effect of beginning-of-year deposits
on the future value accumulated by the end of Hal’s sixty-fifth year.


P5–29 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?
Mixed stream
Beginning of year Cash flow
1 $ 2,000
2 4,000
3 6,000
4 8,000
5 10,000


P5–39 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.


Please answer in excel with one sheet per answer. Also please show work if and when applicable.

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