1. A new automobile costs $30,000. A down payment of $2500. is made at the time of
purchase with the balance financed for 24 months at 6.00% nominal annual interest
compounded monthly. What are the monthly payments? ($1218)
2. A new widget, with a service life of four years, would save $50,000. in production
costs each year. Using a 12.00% nominal annual interest rate, determine the highest price
that could be justified for the widget, i.e., determine the present value of these future
savings. Lump each year’s savings at the end of the year. Work the problem again and
take the saving at the end of each month. ($151,869 and $158,221)
3. Acme is selling 8.00%, $1000. bonds for payment in 15.0 years (face amount of $1000,
coupon rate of 8.00% with a 15-year maturity). That is, the bond will pay 8.00% of the
principle at the end of each year and then 108% at the end of the 15th year. What is the
equivalent cost of a 10.00% bond under the same conditions, i.e., how much would you have
to pay for a 10.00% bond that provides the same income as the 8.00% bond? That is,
determine the present value of the payments from an 8.00% bond, but at a 10.00% interest
rate. Assume the interest is determined only at the end of each year. ($847.88)
4. When you buy your new car, you are offered a $1,000. maintenance contract that will
cover all repair costs for five years on the car. You estimate the following repair
expenses for the car:
Year 1: 0
Year 2: $100.
0 Year 3: $250.
Year 4: $500.
Year 5: $750.
If you could also make an investment with an 8.00% return for five years, would you buy
the maintenance contract or invest your money? Determine the Present Value of the
maintenance contract, based on an 8.00% rate of return: $1,162.14. Therefore you
would buy the contract assuming you’ll keep the car for five years since the present value
of future payments is greater than the present value of the alternative investment at 8%,
i.e. , $ 1000.
5. Determine the monthly payments on a $150,000 mortgage (loan) at 6.00% (annual
interest) compounded (paid) monthly for 30 years. ($899.32). What is total interest paid
over the 30 years? (Total payments less initial present value) How much is paid against
the principle in the first month? (first monthly payment made (above) less interest for
first month (0.50% of principle))
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