Q$1.$

On September $3,2008$ you invested $$1,000$ at the annual risk$-$free rate

of $5\%$ until APR. $18,2009.$ Exactly $228$ days. Calculate the amount you

will receive on APR $18,2009$ if the annual $5\%$ rate is compounded

$3\mathrm{.}1-$ annually;

$3\mathrm{.}2-$ quarterly;

Q$2.$ Using the same data as in Q$1.$ calculate the amount you will receive on

APR $18,2009$ if the annual $5\%$ rate is compounded

$4\mathrm{.}1-$ daily;

$4\mathrm{.}2-$ continuously.

Q$3.$

Q$4.$

Q$5.$

On SEP $1,2005$ you want to buy T$-$bills in an amount of dollars that will

guarantee you $$3,000$ on the T$-$bills maturity on APR. $21,2006.$ Exactly

$233$ days. Calculate the amount of money you need to invest on SEP $1,$

$2005$ if the annual risk$-$free rate of $5\%$ is continuously compounded.

You invest $$100,000$ dollars in an account that pays you an annual rate

of $10\%$ with continuous compounding.

How long will it take for your initial investment to triple itself? The

answer need not be an integer number.

An investment of $$100,000$ yields $$110,000$ in exactly one year.

Calculate the annual rate of return if it were with:

$7\mathrm{.}1$ Annual compounding

$7\mathrm{.}3$ Monthly compounding

$7\mathrm{.}2$ Semiannual compounding

$7\mathrm{.}4$ Continuous compounding.

Q$6.$

You bought a stock for $$\frac{43\mathrm{.}50}{?}$ share and sold it $5$ months later for

$$\frac{41\mathrm{.}75}{?}$ share. Calculate your annual rate of return on this investment:

$8\mathrm{.}1$ Including a $$.\frac{75}{?}$ share dividend

$8\mathrm{.}2$ Without the dividend.

Q$7.$

The annual rate with monthly compounding is $R_{12}=8\%.$

Calculate the equivalent annual rate with:

a$)$ Continuous compounding

b$)$ daily compounding.

Please answer questiona $1$ to $7$