c$)$ The length of time to wait from part $($b$)$ is obviously unreasonable. A more realisticscenario is that you deposit $$10,000$ initially, and then continue to make smallerrecurring monthly deposits. The formula that can determine the account balance is $=((1+)1)+(1+),$where is the final amount after months, is the principal $($initial deposit$),$ is therecurring monthly deposit, and is the monthly rate of return. Note that in this formula,we assume that the annual interest rate is compounded monthly, so a $2\mathrm{.}1\%$ annualinterest rate makes $=0\mathrm{.}02112=0\mathrm{.}00175.$ How much money do you need to depositeach month for the account balance to reach the down payment goal in $5$ years? Roundto the nearest dollar.d$)$ How much money do you need to deposit each month for the account balance to reachthe down payment goal in $8$ years? Round to the nearest dollar.This project was created by Richard Adamse$)$ Now that you have your down payment, the bank agrees to loan you the remainingdifference to purchase a house valued at $$350,000.$ The loan is a $30-$year fixed$-$ratemortgage with an annual interest rate of $7\mathrm{.}8\%.$ To determine how much you should payeach month to fully pay off the mortgage in $30$ years, we use the formula $=(1+)(1+)1,$where is the monthly payment, is the amount borrowed, is the total number ofmonthly payments, and is the monthly interest rate. Like in part $($c$),$ we assume theannual interest rate is compounded monthly, so $=0\mathrm{.}07812=0\mathrm{.}0065.$ What will be yourmonthly payment on this mortgage? Round to the nearest dollar.f$)$ The bank gives you a second option of a lower annual interest rate of $6\mathrm{.}9\%$ for a $15-$yearfixed$-$rate mortgage. What would be the monthly payment on the mortgage under theseterms? Round to the nearest dollar.g$)$ Compare the two mortgage options. What are the advantages and disadvantages ofeach?