1.A series of ten $500 payments are received at the end of each year over a 10-year
period. During the first two years the interest rate was 5% annual compounded monthly.
During the following two years (years 3-4) the interest rate was 6% annual compounded
semiannually. During the last six years (years 5-10) the interest rate was 12%
compounded annually. Show the cash flow and find the present equivalent of this series
2. You are taking out a loan for $50,000. The term of the loan is 10 years, you will make
monthly payments, and the interest rate is 4% annual compounded monthly.
A) Find the monthly payment, the future value, and the annual effective rate.
b) For the above loan, it is expected that the average annual inflation rate will be 3%
annual compounded monthly for the first 5 years and 5% annual compounded monthly
for the last 5 years. Find the annual payments in year 0 constant dollars for each part of
the loan and find the future value in year 0 constant dollars.
3. Ford issued 20 year $1,000 bonds in 2014 with an annual coupon rate of 7.45%. In
2016 after the coupon for 2016 is paid, that bond can be purchased for $1,285. If you
bought this bond, what is the current yield and yield to maturity?
4. I’m looking forward to retiring and recently the Social Security Administration sent me
some information on my options. If I retire at age 62, I will receive $1,792 per month for
life. If I wait until my full retirement age of 66 years and 4 months, I will receive $2,490
per month for life.
a) I think that I can get an investment that pays 4% annual compounded monthly. How
old will I be when the two above options are equal?
b) Long term inflation is projected to be 3% annual compounded monthly. If all of the
above are constant dollars, how old will I be when the two options are equal?
5. To purchase a house, a couple borrows $200,000 at 5% annual interest compounded
monthly. The loan was to be paid off in equal monthly payments over 25 years. At the 5-
year loan anniversary date they paid off the loan.
a) What was the monthly payment amount?
b) Including the monthly payment due at the 5-year loan anniversary date, how much was
needed to pay off the loan?
c) How much total interest had the couple paid when the loan was paid off at the 5-year
loan anniversary date?
d) If they had made all of the payments for 20 years, what is the total interest the couple
would have paid on the loan?
6. Find a single equation for P. You do not need to provide a numerical answer.
7. Nissan is offering a Rogue for $18,588. This can be financed with a down payment of
$2,008.80 and $249 per month for 72 months. What are the monthly, nominal, and
effective interest rates for this purchase?
8. An engineering company has determined that $100,000 per year will be needed to
maintain a new bridge. How much money is needed in a fund today to maintain the
bridge indefinitely if the interest rate is 4.5%?
9. An investor’s projections of future purchasing power needs, based on an estimated
inflation rate of 5% per year, are given in the cash flow diagram below.
0 1 2 3 4 5 6 7 8 9 10 11 12
$ @ year 6
Available investments are expected to yield 6.5% during the first 6 years and 7.5% during
the final 6 years.
a) Use constant-dollar analysis to determine the future worth at year 12 in the same
constant dollars specified above (year 6 dollars).
b) How many actual dollars would need to be invested at t = 0 to achieve the projected
needs under the expected yield rates?
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