You wish to buy a new car. The cost is $$20,000$ and the interest rate is $10\%.$ The dealer gives you $4$ different offers: $1.$ Pay it all off today $2.$ Pay $$2000$ now and $$20,000$ next year $3.$ Don$$t pay a dime this year, but you will need to pay $$5000$ next year and $$20,000$ one year after that. $4.$ Pay according to this schedule: Today: $1000,$ Yr $1$: $2000$ Yr $2$: $3000,$ Yrs $3$: $3000$ Yr $4$: $150005.$ Pay according to this schedule: Today: $0,$ Yr $1$: $0$ Yr $2$: $0$ Yrs $3$: $5000$ Yr $4$: $10000$ Yr $5$: $13,500$ Which deal should you take? Show a quantitative solution to the problemYou have decided to invest in a $5$ year bond.

The way a bond works is that you are making a loan to someone.

After loaning the money to someone $($a company, the government, etc$),$ you will get payments back

every year $($dividend$).$ This is typically a percentage of the total loan $($or bond value$).$ During the last

year, I get my original money back. For example, I have a $20\%$ bond worth $$5.$ My cash flows are:

Yr$0$: $$5($I pay out for the bond$)$

Yr$1$: $$1(20\%)$

Yr$2$: $$1(20\%)$

Yr$3$: $$1(20\%)$

Yr$4$: $$1(20\%)$

Yr$5$: $$1(20\%)($ Final coupon payment$)$

Yr$5$: $$5($maturity date, I get my money back$)$

You are looking at purchasing a $$10,000$ bond that pays $7\%.$ When you purchase the bond, you will also

need to pay a $3\%$ broker's fee when you purchase the bond and to cash it out at maturity.

a$.$ What is the IRR of this deal? Show your work $10$ pts

b$.$ Assume your money is losing value due to a $4\%$ inflation rate. Using ROI, what is your ROI?

Show your work