A bank quotes an interest rate of $14\%$ per annum with quarterly compounding. What is the equivalent rate with $($a$)$ continuous compounding and $($b$)$ annual compounding?

$2.$ What is meant by LIBOR and LIBID. Which is higher?

$3.$ The $6-$month and $1-$year zero rates are both $10\%$ per annum. For a bond that has a life of

$18$ months and pays a coupon of $8\%$ per annum $($with semiannual payments and one

having just been made$),$ the yield is $10\mathrm{.}4\%$ per annum. What is the bond$$s price? What is

the $18-$month zero rate? All rates are quoted with semiannual compounding.

$4.$ An investor receives $$1,100$ in one year in return for an investment of $$1,000$ now.

Calculate the percentage return per annum with:

$($a$)$ Annual compounding

$($b$)$ Semiannual compounding

Interest Rates $97$

$($c$)$ Monthly compounding

$($d$)$ Continuous compounding.

$5.$ Suppose that $6-$month, $12-$month, $18-$month, $24-$month, and $30-$month zero rates are,

respectively, $4\%,4\mathrm{.}2\%,4\mathrm{.}4\%,4\mathrm{.}6\%,$ and $4\mathrm{.}8\%$ per annum, with continuous compounding.

Estimate the cash price of a bond with a face value of $100$ that will mature in

$30$ months and pays a coupon of $4\%$ per annum semiannually.

$6.$ Assuming that zero rates are as in Problem $4\mathrm{.}5,$ what is the value of an FRA that enables

the holder to earn $9\mathrm{.}5\%$ for a $3-$month period starting in $1$ year on a principal of

$$1,000,000?$ The interest rate is expressed with quarterly compounding.

$7.$ The term structure of interest rates is upward$-$sloping. Put the following in order of

magnitude:

$($a$)$ The $5-$year zero rate

$($b$)$ The yield on a $5-$year coupon$-$bearing bond

$($c$)$ The forward rate corresponding to the period between $4\mathrm{.}75$ and $5$ years in the future.

What is the answer when the term structure of interest rates is downward$-$sloping?

$8.$ What does duration tell you about the sensitivity of a bond portfolio to interest rates.

What are the limitations of the duration measure?

$9.$ What rate of interest with continuous compounding is equivalent to $15\%$ per annum with

monthly compounding?

$10.$ A deposit account pays $12\%$ per annum with continuous compounding, but interest is

actually paid quarterly. How much interest will be paid each quarter on a $$10,000$ deposit?