1. You are saving to buy a new house in 7 years. If you invest $4,500 now at 5.5% interest compoundedquarterly, how much money will you have to use for your down payment?2. You have your heart set on buying a new car in 2 years. You invest $3,200 at 3.75% interestcompounded continuously. How much money will have to use for your down payment on your newcar?3. You are a proud new parent of a baby girl. In eighteen years, you will want to help her pay for college.How much do you need to invest now at 4.75% interest compounded monthly so you can help her payfor the $40,000 expense of college?4. After building your new home, you decide you would like to install an in-ground pool in 7 years. Howmuch do you need to invest now at 5.25% interest compounded continuously to have the $30,000 youwill need to build the pool?5. You recently received an inheritance of $11,500 from your grandparents. Which option is the best wayto invest your money and how much better is the best investment? Option A: 5.6% interestcompounded semi-annually for 8 years or Option B: 3.45% interest compounded continuously for 5years.Part A)Part B)Part C)

Answer:Step-by-step explanation:Q1. Use FV formula to get value at year 7FV= PV [tex](1+r)^{t}[/tex]Since it's quarterly compounding, quarterly rate would be (5.5% / 4)= 1.375% and total duration t would be 7*4 = 28 quartersFV= 4,500 [tex](1+0.01375)^{28}  = 4,500 * 1.46576478[/tex]FV= $6,595.94Q2.Future Value with continuous compounding formula; FV= PV[tex]e^{rt}[/tex]Note: the "e" is an exponentialFV= 3,200[tex]e^{0.0375 * 2}[/tex]FV = 3200* 1.0778841FV= $3,440.229Q3.Here, you find Present value; PV = [tex]\frac{FV}{(1+r)^{t} }[/tex]Since it's monthly compounding, monthly rate would be (4.75% / 12)= 0.3958% and total duration t would be 18*12 = 216 monthsPV= [tex]\frac{40,000}{(1+0.003958)^{216} }[/tex]PV= 40,000/2.3472409PV= 17,041.2845Therefore you need to invest $17,041.28.Q4.Use PV with continuous compounding formula here;PV= [tex]\frac{FV}{e^{rt} }[/tex]Note: the "e" is an exponentialPV = [tex]\frac{30,000}{e^{0.0525 * 7} } \\[/tex]PV= 30,000/1.4441198PV = $20,773.8998Therefore, you need to invest $20,773.90 now.Q5.Compare the FV of each option and choose the highest;a.) FV= PV [tex](1+r)^{t}[/tex]Since it's semi-annual compounding, semi-annual rate would be (5.6% / 2)= 2.8% and total duration t would be 8*2 = 16FV = 11,500[tex](1+0.028)^{16}  = 11,500 * 1.555570987[/tex]FV= $17,889.07b.)Future Value with continuous compounding formula; FV= PV[tex]e^{rt}[/tex]Note: the "e" is an exponentialFV= 11,500[tex]e^{0.0345 * 5}[/tex]FV= 11,500 * 1.188271821FV= $13,665.126Therefore, Option A is a better option by $4,223.94