Annuity Payment and EAR

You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 4 years (48 months), and the nominal interest rate would be 6%, with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.

$

What is the loan's EFF%? Do not round intermediate calculations. Round your answer to two decimal places.

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Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) Do not round intermediate calculations. Round your answers to the nearest cent.

An initial $600 compounded for 1 year at 8%.

$

An initial $600 compounded for 2 years at 8%.

$

The present value of $600 due in 1 year at a discount rate of 8%.

$

The present value of $600 due in 2 years at a discount rate of 8%.

$

Use both the TVM equations and a financial calculator to find the following values. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) Do not round intermediate calculations. Round your answers to the nearest cent.

An initial $500 compounded for 10 years at 8%.

$

An initial $500 compounded for 10 years at 16%.

$

The present value of $500 due in 10 years at an 8% discount rate.

$

The present value of $500 due in 10 years at a 16% discount rate.

$

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. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.) Do not round intermediate calculations. Round your answers to the nearest cent.

$800 per year for 10 years at 14%.

$

$400 per year for 5 years at 7%.

$

$800 per year for 5 years at 0%.

$

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Future value of $800 per year for 10 years at 14%: $

Future value of $400 per year for 5 years at 7%: $

Future value of $800 per year for 5 years at 0%: $

Find the present value of the following ordinary annuities. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press PV, and find the PV of the annuity due.) Do not round intermediate calculations. Round your answers to the nearest cent.

$200 per year for 10 years at 10%.

$

$100 per year for 5 years at 5%.

$

$200 per year for 5 years at 0%.

$

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Present value of $200 per year for 10 years at 10%: $

Present value of $100 per year for 5 years at 5%: $

Present value of $200 per year for 5 years at 0%: $

Find the present values of the following cash flow streams. The appropriate interest rate is 12%. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator's cash flow register, you must enter CF₀ = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the Ch04 Tool Kit.xlsx.) Do not round intermediate calculations. Round your answers to the nearest cent.

Year	Cash Stream A	Cash Stream B
1	$100	$300
2	400	400
3	400	400
4	400	400
5	300	100

Stream A: $

Stream B: $

What is the value of each cash flow stream at a 0% interest rate? Round your answers to the nearest dollar.

Stream A $

Stream B $

Find the amount to which $300 will grow under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

6% compounded annually for 5 years.

$

6% compounded semiannually for 5 years.

$

6% compounded quarterly for 5 years.

$

6% compounded monthly for 5 years.

$

Find the present value of $500 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

12% nominal rate, semiannual compounding, discounted back 5 years.

$

12% nominal rate, quarterly compounding, discounted back 5 years.

$

12% nominal rate, monthly compounding, discounted back 1 year.

$

Find the future values of the following ordinary annuities.

FV of $200 each 6 months for 9 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

FV of $100 each 3 months for 9 years at a nominal rate of 8%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

The annuities described in parts a and b have the same amount of money paid into them during the 9-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the 9 years. Why does this occur?