Financial management(BSM-410) problem solving

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5-1 FUTURE VALUE If you deposit $2,000 in a bank account that pays 6% interest annually, how
much will be in your account after 5 years?
5-7 PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An investment will pay $150 at
the end of each of the next 3 years, $250 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 11% annually, what is its
present value? Its future value?
5-9 PRESENT AND FUTURE VALUES FOR DIFFERENT PERIODS Find the following values using the
equations and then a financial calculator. Compounding/discounting occurs annually.
A. An initial $600 compounded for 1 year at 6%
B. An initial $600 compounded for 2 years at 6%
C. The present value of $600 due in 1 year at a discount rate of 6% d. The present value of
$600 due in 2 years at a discount rate of 6%
5-10 PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES Find the following values.
Compounding/discounting occurs annually.
A.
B.
C.
D.
An initial $200 compounded for 10 years at 4%
An initial $200 compounded for 10 years at 8%
The present value of $200 due in 10 years at 4%
The present value of $1,870 due in 10 years at 8% and at 4%
5-28 NOMINAL INTEREST RATE AND EXTENDING CREDIT As a jewelry store manager, you want
to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you
must borrow funds from your bank at a nominal 9%, monthly compounding. To offset your
overhead, you want to charge your customers an EAR (or EFF%) that is 3% more than the bank
is charging you. What APR rate should you charge your customers?
5-29 BUILDING CREDIT COST INTO PRICES Your firm sells for cash only, but it is thinking of
offering credit, allowing customers 90 days to pay. Customers understand the time value of
money, so they would all wait and pay on the 90th day. To carry these receivables, you would
have to borrow funds from your bank at a nominal 9%, daily compounding based on a 360-day
year. You want to increase your base prices by exactly enough to offset your bank interest cost.
To the closest whole percentage point, by how much should you raise your product prices?
5-41 TIME VALUE OF MONEY Answer the following questions:
A. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years.
B. What is the investment’s FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5
years?
C. Find the PV of $1,000 due in 5 years if the discount rate is 10%.
D. What is the rate of return on a security that costs $1,000 and returns $2,000 after
5 years?
E. Suppose California’s population is 40 million people and its population is
expected to grow by 2% annually. How long will it take for the population to
double?
F. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if
the interest rate is 15%. What is the annuity’s FV?
G. How will the PV and FV of the annuity in part f change if it is an annuity due?
H. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is
10%, semiannual compounding?
I. What will the annual payments be for an ordinary annuity for 10 years with a PV
of $1,000 if the interest rate is 8%? What will the payments be if this is an annuity
due?
J. Find the PV and the FV of an investment that pays 8% annually and makes the
following end-of-year payments:
K. Five banks offer nominal rates of 6% on deposits, but A pays interest annually, B
pays semiannually, C pays quarterly, D pays monthly, and E pays daily.
1. What effective annual rate does each bank pay? If you deposit $5,000 in each bank
today, how much will you have in each bank at the end of 1 year? 2 years?
2. If all of the banks are insured by the government (the FDIC) and thus are equally risky,
will they be equally able to attract funds? If not (and the TVM is the only consideration),
what nominal rate will cause all of the banks to provide the same effective annual rate
as Bank A?
3. Suppose you don’t have the $5,000 but need it at the end of 1 year. You plan to make a
series of deposits—annually for A, semiannually for B, quarterly for C, monthly for D,
and daily for E—with payments beginning today. How large must the payments be to
each bank?
4. Even if the five banks provided the same effective annual rate, would a rational investor
be indifferent between the banks? Explain.
l. Suppose you borrow $15,000. The loan’s annual interest rate is 8%, and it requires
four equal end-of-year payments. Set up an amortization schedule that shows the
annual payments, interest payments, principal repayments, and beginning and ending
loan balances.