TVM Problems Set #$2$Write your answers in theNAMEand indicate your inputs after the questions. Due in class at $1$:$00$ on October$8,2024\mathrm{.}1.$ You invest $$4,000$ today in a savings account paying $5\%.$ How much will you have in your account at the end of $5$ years: a$)$With annual compounding?b$)$With monthly compounding?$2.$Sam decides to invest $$1000$ per year for $5$ years. How much will he have in his account ifinterest is compounded annually?What will the ending balance be in $15$ years if an investment is made of $$10,000$ today andit earns $11\%$ compounded monthly?$4.$Virginia can buy a piece of property for $$6500$ cash OR for $$3000$ down and $$4000$ in $3$years. If money is earning $6\%$ compounded annually, which is the better purchase plan? $($Which has the lowest PV$)5.$Betsy can purchase a piece of property for $$3550$ cash OR for $$5000$ in $12$ months. Which is the better plan if she is earning $9\%$ on her money, compounded monthly?$6.$How much should Lauren pay for an annuity of $$5,000$ per year for $10$ years assuming$6\mathrm{.}5\%$ interest compounded annually?Dr$.$ and Mrs$.$ McNamara want to provide for a $$5000$ scholarship every year forever. Ifthe school can get a $5\mathrm{.}5\%$ return on its investment, how much money should they donate now for this perpetuity?Knox makes a $$2000$ annual deposit into a mutual fund that produces a return of $12\%$annually for $3$ years. How much will Knox have at the end of the three$-$year term?$9.$Mazie saves $$1000$ per month in an IRA account for $30$ years at $5\%$ interest compoundedmonthly. How much will Mazie have at the end of $30$ years?$10.$Assume Murfreesboro's population is expected to increase at a rate of $4\%$ per year for thenext ten years. If the current population is $150,000,$ what is the expected population at the end of the next ten years?