$-$create a PDF Rmarkdown generated document, an Rscript document clearly explaining the code that is being run, and the corresponding Rmd file.

For each question, you must show the code that generates the answer.$$The document must look organized and be self$-$explanatory. $-$

Pricing debt Instruments.

Please price the following projects and debt instruments.$-$Please be sure to follow the instructions for each item. For each question, you must show the calculation of the result, you should not just show the final

number but also the process.$$ Question $1$: What is the future value $($FV $)$ of $1,800$ USD in $85$ years with an interest rate of $7\mathrm{.}0\%?$ Question $2$: What is the present value $($PV $)$ of $13,900$ USD received in $98$ years when the interest

rate is $13\mathrm{.}5\%?$Question $3$: What is the future value $($FV $)$ of $10,700$ USD in $18$ years and $7$ days with an interest

rate of $19\mathrm{.}0\%?$Question $4$: Calculate the PV of investment with cash flows: $1,000,1,300,400,-100,$ and $1,000$ USD received in $2,3,14,15,$ and $16$ years with a $11\mathrm{.}5\%$ discount rate. Please present these results in a nice,

well$-$formatted table that shows or each maturity: the interest rate, cash flow, the present vale formula for each calculation and, the present value for each cash flow. Then, please also show the present value of the entire project in the final row of the table. $.$Question $5$: Calculate the PV of investment with cash flows:$1,200,-200,-500,$ and $400$ USD received in $4,15,16,$ and $17$ years with discount rates $17\mathrm{.}3\%,17\mathrm{.}3\%,19\mathrm{.}2\%,$ and $18\mathrm{.}1\%.$ Please present these results in a nice, well$-$formatted table that shows or each maturity: the interest rate, cash flow, the

present vale formula for each calculation and, the present value for each cash flow. Then, please also show the present value of the entire project in the final row of the table. $50$ points$$Question $6$: What is the present value $($PV $)$ of a fixed payment loan with yearly fixed payments of $26,000$ USD and a time to maturity of $12$ years when the interest rate is $2\mathrm{.}0\%?$Question $7$: What is the yearly fixed payment $($FP$)$ of a fixed payment loan with a loan value $($LV $)$of $97,000$ USD and a time to maturity of $15$ years when the interest rate is $2\mathrm{.}0\%?$Question $8$: What is the present value $($PV $)$ of a $19\mathrm{.}5\%$ coupon bond with face value $140,000$ USD and a time to maturity of $80$ years when coupon payments are yearly and interest rate is $11\mathrm{.}0\%$ Question $9$: What is the present value $($PV $)$ of a perpetuity with a yearly coupon payment of $16,700$USD when the interest rate is $8\mathrm{.}5\%?10$ points$$Question $10$: What is the present value $($PV $)$ of a discount bond with face value $61,000$ USD due in

$67$ years when interest rates are $11\mathrm{.}5\%?$Question $11$: What is the yield to maturity $($Y TM$)$ of a discount bond with face value $94,000$ USD due in $23$ years sold at $82,480$ USD?$$Question $12$: What is the yield to maturity $($Y TM$)$ of a perpetuity with a yearly coupon payment of $16,500$ USD sold at $136,140$ USD?$$Question $13$: What is the yield to maturity $($Y TM$)$ of a fixed payment loan with yearly fixed payments

of $111,000$ USD and a time to maturity of $54$ years sold at $700,510$ USD?.Question $14$: What is the yield to maturity $($Y TM$)$ of a $13\mathrm{.}0\%$ annual coupon bond with face value $52,000$ USD and a time to maturity of $93$ years sold at $88,560$ USD?$$Question $15$: Calculate one$-$year returns $($R$)$ over $6$ years of a $7\mathrm{.}5\%$ annual coupon bond with face value $137,000$ USD and initial time to maturity of $40$ years. The initial interest rate is $4\mathrm{.}20\%,$ but it changes to $9\mathrm{.}70\%,4\mathrm{.}70\%,8\mathrm{.}50\%,4\mathrm{.}00\%,4\mathrm{.}00\%,$ and $7\mathrm{.}10\%$ after $1,2,3,4,5,$ and $6$ years. Please show these results in a nicely formatted table, where we can see the results for each year.

$-$Mortgages and their cost over time

In this exercise, we will analyze how mortgages and their real value have changed over time. For this, you will have to$-$obtain the following series from the Federal Reserve Bank of St Louis$1$: $30-$Year Fixed Rate Mortgage Average in the United States$$Consumer Price Index for All Urban Consumers: All Items in U$.$S$.$ City Average$$ Consumer Price Index for All Urban Consumers: Shelter in U$.$S$.$ City Average$$Average Sales Price for New Houses Sold in the United States$5$

Please follow these instructions to conduct your analysis:$1)$Obtain these series with the $$quantmod$$ R package. If you get them by downloading their excel and

importing it$,$ you will not get the points out of this exercise. Please show the code of this import too. $2)$The $30-$Year Fixed Rate Mortgage Average data is reported weekly. Please summarize it into a monthly dataset. Please show the code that does this, and show that you executed this correctly by showing the first $20$ observations of the resulting dataset