Assume compound interest unless otherwise stated. Must be solved with factors and$/$or Excel PV$,$ FV$,$ PMT$,$ NPER, or interest rate functions; you may not use NPV$.$

Formulation $($including factors$)/$ calculations must be shown. For each problem, include a cash flow diagram. If Excel is used for calculations, include the Excel formula$($s$)$ used.

a$.$ A investor will provide you $$40,000$ today for a business venture. In exchange, they want an annual payment of

$"$A$"$ for each of the next $10$ years, at $12\%$ interest. What is $A?$

b$.$ You put $$20,000$ per year $($starting at time $1)$ into an index firm earning a $10\%$ rate of return for $20$ years. How

much money will you have in the fund at the end of $20$ years?

c$.$ A new expanded production line will bring in $$50,\frac{000}{?}$ year in new revenues and cost savings for the next $8$

years. At $15\%$ interest, how much would you be willing to spend now on building the new line so as to break

even on this investment?