3a Time for a Lump Sum to Double

How long will it take $200 to double if it is deposited and earns the following rates? Round your answers to the closest year. [Notes: (1) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV = -200, PMT = 0, FV = 400, and I = 7 in an HP-12C and then press the N key, you will get 11 years. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP10BII gives the exact answer; (2) 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.]

7.3%. year(s)

11.2%. year(s)

17.2%. year(s)

100%. year(s)

3b

Future Value of an Annuity

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. Round your answers to the nearest cent. (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.)

$600 per year for 10 years at 6%. $

$300 per year for 5 years at 3%. $

$600 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.

$600 per year for 10 years at 6%. $

$300 per year for 5 years at 3%. $

$600 per year for 5 years at 0%. $

3c Present Value of an Annuity

Find the present value of the following ordinary annuities. Round your answers to the nearest cent. (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.)

$200 per year for 10 years at 12%. $

$100 per year for 5 years at 6%. $

$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.

$200 per year for 10 years at 12%. $

$100 per year for 5 years at 6%. $

$200 per year for 5 years at 0%. $

3d Uneven Cash Flow Stream

Find the present values of the following cash flow streams. The appropriate interest rate is 13%. Round your answers to the nearest cent. (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 Chapter 4 Tool Kit.)

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 cent. Stream A $ Stream B $

3f Effective Rate of Interest

Find the interest rate (or rates of return) for each of the following situations. Round your answers to two decimal places.

You borrow $700 and promise to pay back $763 at the end of 1 year. %

You lend $700 and receive a promise to be paid $763 at the end of 1 year. %

You borrow $80,000 and promise to pay back $135,204 at the end of 12 years. %

You borrow $10,000 and promise to make payments of $2,445.7 at the end of each year for 5 years. %

3g Future Value for Various Compounding Periods

Find the amount to which $450 will grow under each of the following conditions. Round your answer to the nearest cent.

11% compounded annually for 5 years $

11% compounded semiannually for 5 years $

11% compounded quarterly for 5 years $

11% compounded monthly for 5 years $

3f Present Value for Various Compounding Periods

Find the present value of $675 due in the future under each of the following conditions. Round your answers to the nearest cent.

6% nominal rate, semiannual compounding, discounted back 5 years $

6% nominal rate, quarterly compounding, discounted back 5 years $

6% nominal rate, monthly compounding, discounted back 1 year $

3j Effective versus Nominal Interest Rate

Universal Bank pays 7% interest, compounded annually, on time deposits. Regional Bank pays 6%, compounded quarterly.

Based on effective interest rates, in which bank would you prefer to deposit your money?

I. You would choose Regional Bank because its EAR (or EFF%) is higher. II. You are indifferent between the banks and your decision will be based upon which one offers you a gift for opening an account. III. You would choose Universal Bank because its EAR (or EFF%) is higher. IV. You would choose Regional Bank because its nominal interest rate is higher. V. You would choose Universal Bank because its nominal interest rate is higher.

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 any interest. I. If funds must be left on deposit until the end of the compounding period (3 months for Universal Bank and 1 year for Regional Bank), and you think there is a high probability that you will make a withdrawal during the year, then Regional Bank might be preferable. II. If funds must be left on deposit until the end of the compounding period (1 year for Universal Bank and 3 months for Regional Bank), and you have no intentions of making a withdrawal during the year, then Regional Bank might be preferable. III. If funds must be left on deposit until the end of the compounding period (1 year for Universal Bank and 3 months for Regional Bank), and you think there is a high probability that you will make a withdrawal during the year, then Universal Bank might be preferable. IV. If funds must be left on deposit until the end of the compounding period (3 months for Universal Bank and 1 year for Regional Bank), and you think there is a high probability that you will make a withdrawal during the year, then Universal Bank might be preferable. V. If funds must be left on deposit until the end of the compounding period (1 year for Universal Bank and 3 months for Regional Bank), and you think there is a high probability that you will make a withdrawal during the year, then Regional Bank might be preferable.