$1)$ Uneven Cash Flow Stream

a$.$ Find the present values of the following cash flow streams. The appropriate interest rate is $10\%.($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 CF$0=0.$ Note also that it is quite easy to work the problem with Excel, using procedures described in the Ch$04$ Tool Kit.xlsx$.)$ Do not round intermediate calculations. Round your answers to the nearest cent.

Year Cash Stream A Cash Stream B

$1$ $$100$ $$250$

$2400400$

$3400400$

$4400400$

$5250100$

Stream A: $ $\_\_\_\_$

Stream B: $ $\_\_\_\_$

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 $ $\_\_\_\_$

$2)$ Effective Rate of Interest

Find the interest rate $($or rates of return$)$ in each of the following situations. Do not round intermediate calculations. Round your answers to the nearest whole number.

a$.$ You borrow $$720$ and promise to pay back $$756$ at the end of $1$ year.

$\_\_\_\_\%$

b$.$ You lend $$720$ and receive a promise to be paid $$756$ at the end of $1$ year.

$\_\_\_\_\%$

c$.$ You borrow $$70,000$ and promise to pay back $$295,837$ at the end of $11$ years.

$\_\_\_\_\%$

d$.$ You borrow $$8,000$ and promise to make payments of $$2,219\mathrm{.}30$ at the end of each of the next $5$ years.

$\_\_\_\_\%$

$3)$ Future Value for Various Compounding Periods

Find the amount to which $$600$ will grow under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

a$.12\%$ compounded annually for $5$ years.

$ $\_\_\_\_$

b$.12\%$ compounded semiannually for $5$ years.

$ $\_\_\_\_$

c$.12\%$ compounded quarterly for $5$ years.

$ $\_\_\_\_$

d$.12\%$ compounded monthly for $5$ years.

$ $\_\_\_\_$

$4)$ Present Value for Various Compounding Periods

Find the present value of $$350$ due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

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

$ $\_\_\_\_$

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

$ $\_\_\_\_$

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

$ $\_\_\_\_$