FINANCE PROBLEM ASSIGNMENT

FINANCE PROBLEM

1.
Future Value — If you deposit $10,000 in a bank account that pays 10 percent
interest annually, how much would be in your account after 5 years?

2. Present Value — What is the present value of a security that will pay
$5,000 in 20 years if securities of equal risk pay 7 percent annually?

3.
Your parents are planning to retire in 18 years. They currently have $250,000 and they would
like to have $1,000,000 when they retire.
What annual rate of interest would they have to earn on their $250,000
in order to reach their goal, assuming they save any additional funds?

4.
If you deposit money today into an account that pays 6.5 percent interest, how
long will it take for you to double your money?

5. You have $42,180.53 in a brokerage
account, and you plan to deposit an additional $5,000 at the end of every
future year until your account totals $250,000. You expect to earn 12% annually
on the account. How many years will it take to reach your goal?

6. What is the future value of a 7%, 5-year
that pays $300 each year? If this were an annuity due, what would its future
value be?

7. Present And Future Values Of A Cash Flow
Stream: An investment will pay $100 at the end of each of the next 3 years,
$200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of
Year 6. If other investments of equal risk earn 8% annually, what is its
present value? Its future value?

8. You want to buy a car, and a local bank
will lend you $20,000. The loan will be fully amortized over 5 years You want to buy a car, and a local bank will
lend you $20,000. The loan would be fully amortized over 5 years (60 months),
and the nominal interest rate would be 12 percent, with interest paid monthly.
What would be the monthly loan payment? What would be the loan’s EFR%?

9. Find the
following equations, then work the problems using a financial calculator

4-9) Find the
following values, using the equations, and then work the problems using a
financial calculator to check your answers. Disregard rounding differences.
a. An initial $500 compounded for 1 year at 6%
$530.00
b. An initial $500 compounded for 2 years at 6%
$561.80
c. The present value of $500 due in 1 year at a discount rate of 6%
$471.70
d. The present value of $500 due in 2 years at a discount rate of 6%
$445.00

(4-11) To the closest year, how long will it take $200 to double if it is
deposited and earns the following rates?
a. 7%
10 years
b. 10%
7 years
c. 18%
4 years
d. 100%
1 year

(4-12) Find the future value of the following annuities. The first payment in
these annuities is made at the end of Year 1, so they are ordinary annuities.
a. $400 per year for 10 years at 10%
$6,374.97
b. $200 per year for 5 years at 5%
$1,105.13
c. $400 per year for 5 years at 0%
$2,000.00
d. Now rework parts a, b, and c assuming that payments are made at the
beginning of each year, that is they are annuities due.
1. $7,012.61
2. $1,160.38
3. $2,000.00

(4-13) Find the present value of the following ordinary annuities.
a. $400 per year for 10 years at 10%
$2,457.83
b. $200 per year for 5 years at 5 %
$865.90
c. $400 per year for 5 years at 0%
$2,000.00
d. Now rework parts a, b, and c assuming that payment are made at the beginning
of each year; that is, they are annuities due.
1. $2,703.61
2. $909.19
3. $2,000.00

(4-14) Find the present values of the following cash flows streams. The
appropriate interest rate is 8%.
Year Cash Stream A Cash Stream B
1 $100 $300
2 400 400
3 400 400
4 400 400
5 300 100
PVA = $1,251.25
PVB = $1,300.32
b. What is the value of each cash flow stream at a 0% interest rate?
PVA = $1,600.00
PVB = $1,600.00

15. Find the interest rates earned on each
of the following:
a. you borrow $700 and promise to pay back $749 at the end of year 1.
b. you lend $700 and the borrower promises to pay you $749 at the end of year
1.
c. you borrow $85,000 and promise to pay back $201,229 at the end of 10 years.
d. you borrow $9,000 and promise to make payments of $2,684.80 at the end of
each year for 5 years.

16. Find the amount to which $500 will grow
under each of the following conditions.

a. 12%
compounded annually for 5 years
b. 12%
compounded semiannually for 5 years
c. 12%
compounded quarterly for 5 years
d. 12%
compounded monthly for 5 years

17. Find the present value of $500 due in
the future under each of the conditions.

a. 12% nominal rate, semiannual compounding, discounted back 5 years
b. 12% nominal rate, quarterly compounded, discounted back 5 years
c. 12% nominal rate, monthly compounding, discounted back 1 year.

18. Find the future values of the following
ordinary annuities.

a. FV $400 paid each 6 months for 5 years at a nominal rate of 12%, compounded
semiannually
b. FV $200 each 3 months for 5 years at a nominal rate of 12%, compounding
quarterly
c. The annuities described in parts and b have the same total amount of money
paid into them during the 5 year period and both earn interest at the same
nominal rate, yet the annuity in part b ends up larger than the one in part b
earns $101.75 more than the one in part a over the 5 years. why does this
occur?

19. Universal Bank pays 7 percent interest,
compounded annually, on time deposits. Regional Bank pays 6 percent
interest, compounded quarterly.
a. Based on effective interest rates, in which bank would you prefer to deposit
your money? Why
b. Could your choice of banks be influenced by the fact that you might want to
withdraw your funds during the year as opposed to at the end of the
year? In answering this question, assume that funds must be left on
deposit during the entire compounding period in order for you to receive
interest.

20. a. Set up an amortization schedule for a $25,000 loan to be repaid in equal
installments at the end of each of the next 5 years. The interest rate is 10%.
b. How large must each annual payment be if the loan is for $50,000? Assume
that the interest rate remains at 10% and that the loan is still paid off over
5 years.
c. How large must each payment be if the loan is for $50,000, the interest rate
is 10%, and the loan is paid off in equal installments at the end of each of
the next 10 years? This loan is for the same amount as the loan in part b, but
the payments are spread out over twice as many periods. Why are these payments
not half as large as the payments on the loan in part b?

21. Sales for Hanebury Corporation’s just-ended year were $12 million. Sales
were $6 million 5 years earlier.
a) at rate did sales grow
b)Suppose someone calculated the sales growth for Hanebury in part a as
follows: “Sales doubled in 5 years. This represents a growth of 100% in 5
years; dividing 100% by 5 results in an estimated growth rate of 20% per year.”
Explain what is wrong with this calculation.

22. Washington-Pacific invests $4 million
to buy a tract of land and plant some young pine trees. The trees can be
harvested in 12 years, at which time W-P plans to sell the forest at an
expected price of $8 million. What is W-P’s expected rate of return?

23. A mortgage company offers to lend you
$85,000; the loan calls for payments of $8,273.59 at the end of each year for
30 years. What interest rate is the mortgage company charging you?

24. To complete your last year in business
school and then go through law school, you will need $10,000 per year for 4
years, starting next year (that is you will need to withdraw the first $10,000
one year from today). Your rich uncle offers to put you through school, and he
will deposit in a bank paying 7% interest a sum of money that is sufficient to
provide the 4 payments of $10,000 each. His deposit will be made today.

a. How large must the deposit be?
b. How much will be in the account immediately after you make the first
withdrawal? After the last withdrawal?

25. While Mary Karen was a student at the
University of Tennessee, she borrowed $12,000 in student loans at an annual
interest rate of 9%. If Mary repays $1,500 per year, then how long (to the
nearest year) will it take her to repay the loan?

26. You need to accumulate $10,000. To do
so, you plan to make deposits of $1,250 per year, with the first payment being
made a year from today, in a bank account which pays 12 % interest, compounded
annually. Your last deposit will be less than $1,250 if less is needed to round
out to $10,000. How many years will it take you to reach your $10,000 goal, and
how large will the last deposit be?

27. What is the present value of a
perpetuity of $100 per year if the appropriate discount rate is 7%? If interest
rates in general were to double and the appropriate discount rate rose to 14%,
what would happen to the present value of the perpetuity?

28. Assume that you inherited some money. A
friend of yours is working as an unpaid intern at a local brokerage firm, and
her boss is selling securities that call for 4 payments of $50 (1 payment at
the end of each of the next 4 years) plus an extra payment of $1,000 at the end
of Year 4. Your friend says she can get you some of these securities at a cost
of $1,025 each. Your money is now invested in a bank that pays an 10% nominal
(quoted) interest rate but with quarterly compounding. You regard the
securities as being just as safe, and as liquid, as your bank deposit, so your
required effective annual rate of return on the securities is the same as that
on your bank deposit. You must calculate the value of the securities to decide
whether they are a good investment. What is their present value to you?

29. Assume that your aunt sold her house on
December 31, and to help close the sale she took a second mortgage in the
amount of $40,000 as part of the payment. The mortgage has a quoted (or
nominal) interest rate of 10%, but it calls for payments every 6 months,
beginning on June 30, and is to be amortized over 10 years. Now, 1 year later,
your aunt must inform the IRS and the person who bought the house about the
interest that was included in the two payments made during the year. (This
interest will be income to your aunt and a deduction to the buyer of the
house.) To the closest dollar, what is the total amount of interest that was
paid during the first year?