For each of the problems below, draw a cash flow diagram and solve for the appropriate variable using:

Formulas, and $2)$ Excel $($NO Interest Table solving required$).$

VTEPS, Inc. has decided to provide your team $$200,000$ today for your BRG efforts. It expects you to repay this at the end of $5$ years with a $12\%$ annual interest rate. What is the amount that you will repay in $5$ years?

What if VTEPS, Inc. requested that you repay this every year for $5$ years. How much would you repay each year?

What if VTEPS, Inc. wants two equal payments at the end of years $4$&$5$ only? What is the amount of these two payments?

You have approached leadership at VTEPS, Inc. and assured them that your BRG can provide the company $$250,000$ at the end of $5$ years. How much are you requesting from them today, if VTEPS, Inc. expects at $15\%$ annual interest rate?

Your team has approached management at VTEPS, Inc. and assured them that your BRG can provide the company $$50,000$ every year for $5$ years. How much are you requesting from them today, if VTEPS, Inc. expects at $15\%$ annual interest rate?

VTEPS, Inc. management is willing to provide your team $$200,000$ today, if your team is able to return $$457,551\mathrm{.}55$ at the end of $5$ years. What interest rate is VTEPS, Inc. expecting?

VTEPS, Inc. management is willing to provide your team $$200,000$ today, if your team is able to return $$59,663\mathrm{.}11$ every year for $5$ years. What interest rate is VTEPS, Inc. expecting?

VTEPS, Inc. management is willing to provide your team $$200,000$ today, if your team is agrees to pay a lump sum of $$450,000$ at the end and an interest rate of $16\%.$ How much time does your team have to repay this? What if VTEPS, Inc. wanted $12\%?20\%?$

VTEPS, Inc. is planning to purchase a plece of equipment that is expected to last $50$ years. Maintenance costs are $$1,000$ each year for the first $ years, followed by a $$10,000$ cost at the end of year $15$ and a $$10,000$ cost at the end of year $30.$ Using an interest rate of $10\%$ per year, what amount should VTEPS, Inc. budget on an annual basis for all $50$ years?

It is estimated that a certain piece of equipment for your BRG project can save VTEPS, Inc. $$22,000$ per year in labor and materials cost. The equipment has an expected life of five years and no market value. If VTEPS, Inc. must earn a $15\%$ annual return on such investments, how much could be justified now for the purchase of this piece of equipment?