Assignment $2,$ Part B$-1$

Notes: When reporting interest rates and related values, please use the rounding rules that are down below. Interest rates and growth rates should be reported in percent, although you'll usually calculate them as decimal values. Discount ratios, return ratios and annual return ratios should not be reported in percent: they can be reported in the same $($decimal$)$ form in which they're calculated.

For help with the assignment, please see the Reference notes $($Refnotes$.$pdf$),$ pp$.1-4,$ and my first set of Topic $2-$B lecture notes $($Lectures$2-$B$1.$pdf$).$ Both items will be available in Canvas.

Question $1,$ unlike Questions $2$ and $3,$ does not primarily require doing calculations. Instead, you'll be translating my in$-$words descriptions of credit instruments into symbolic descriptions, using the notation for describing credit instruments presented in my lectures and notes. A few calculations may be necessary, but they aren't the main component of the answers required.

ROUNDING RULES

In the case of interest rates and related values, round to the third decimal place, which is the nearest tenth of a percent. Examples: round $0\mathrm{.}0746139$ to $0\mathrm{.}075,$ which is $7\mathrm{.}5$ percent and should be reported in that way. And round $1\mathrm{.}1386529$ to $1\mathrm{.}139.$

Do the same thing for discount ratios, return ratios and annual return ratios, which should not be reported in percent.

In the case of a dollar figure greater than $$1000,$ round to the nearest dollar. Example: round $$23453\mathrm{.}29874$ to $$23,453.$

In the case of a dollar figure less than $$1000,$ round to the nearest cent. Example: round $$97\mathrm{.}335914$ to $$97\mathrm{.}34.$

If you need to use an answer from one question to help you calculate the answer to another question, feel free to use the rounded version of the first answer.

Notation

Translate the following descriptions of credit instruments into the notation used in class.

Note: For the credit instruments in Parts A$-$C and F$,$ you do not need to provide a complete mathematical description of the payment on the credit instrument in each year. For the credit instruments in Parts D and E$,$ you do need to do so$.$

$1.$a$.$ A credit instrument with a five$-$year term costs $$10,000$ and returns a single payment of $$15,000$ at maturity.

$1.$b$.$ A credit instrument with a term of three months costs $$99,250.$ It returns a single payment of $$100,000$ at maturity.

$1.$c$.$ A credit instrument costs $$50,000.$ It returns a payment of $$35,000$ after two years, a payment of $$40,000$ after five years, and a $($final$)$payment of $$25,000$after ten years.

$1.$d$.$ A principal$-$and$-$interest credit instrument with a term of twelve years costs $$9000.$ It has a face value of $$10,000$ and a coupon rate of $4$ percent.

$1.$e$.$ An annuity costs $$750,000.$ It returns a payment of $$100,000$ at the end of each of the next ten years.

$1.$f$.$ A credit instrument with a term of nine years costs $$250,000.$It returns a payment at the end of every third year after it is issued. The first payment is $$180,000.$ Each subsequent payment is a third smaller$($two$-$thirds as large as$)$ the preceding payment.

$2.$ Calculating return rates

Calculate the discount ratio, return ratio, annual return ratio and annual rate of return $($interest rate$)$ for each of the following credit instruments.

Note: As indicated in the introduction, the annual interest rate should be reported in percent, but the other values should not be$.$ Unless otherwise indicated, round the values to three decimal places, if they have that many. For the annual interest rate, that amounts to rounding to the nearest tenth of a percent.

$2.$a$.$ The credit instrument from Question $1-$A$.$

$2.$b$.$ A credit instrument that has a four$-$year term, costs $$20,000,$and returns a single payment of $$25,000$ at maturity.

$2.$c$.$ A credit instrument that has a two$-$year term, costs $$9000,$ and returns a single payment of $$10,000$ at maturity.

$2.$d$.$A credit instrument that has a one$-$year term, costs $$950,$ and returns a single payment of $$1000$ at maturity.

$2.$e$.$The credit instrument from Question $1-$B$.$

$2.$f$.$ A single$-$payment credit instrument that costs$$42,000$ and returns$$50,000$ after $30$ months.

$3.$ Interest rates and growth rates

Calculate the annual growth rate of each of the following items. Report the growth rates in percent. Unless otherwise indicated, round to the nearest tenth of a percent.

Hint: In each case, calculate the time interval between the two values, measured in years, possibly including fractions of a year. Use it as the "term."

$3.$a$.$Worldwide iPhone sales, which were $39\mathrm{.}99$ million in $2010$ and $231\mathrm{.}22$ million in $2015.$

$3.$b$.$The population of India, which was $376\mathrm{.}3$ million in $1950$ and $1406\mathrm{.}6$ million in $2022.$

$3.$c$.$The U$.$S$.$ national $($federal government$)$ debt, which was $$8507$ billion in $2006$ and $$29,617$ billion in $2021.$

$3.$d$.$ The U$.$S$.$ Consumer Price Index, which was $257\mathrm{.}0$ in December $2019,$shortly before the pandemic began, and $296\mathrm{.}3$ in June $2022($Hint: How many months are there from December $2019$ to June $2022,$ counting January $2019$ as the first month?$)$