in R.

4. Suppose we have two investment contracts, one is Single Interest, another one is Com- pound Interest, in the formula, P is initial investment, r is interest rate, t is time(in year), A is total amount you get after t years. Ag = P + (1+r9*t) Ac = P*e"c*t (a) (10 points) Write two functions called Totals and Totalc to calculate the total amount you can get after t years, your input should include P, r and t. (b) (10 points) Suppose now you have 10,000 dollars, and the single interest rate is 6% each year, the compound interest rate is 4.5% each year. If we need 15,000 dollars to buy a car, which way is faster to get 15,000? and when can you buy the car? (If you get a fraction or decimal, round to the next integer.) (c) (15 points) Write another function, compare two contracts and calculate how much more you can get after t years using the better contract, print the better way (single or compound) and the difference. Your input should include P, rs, re and t. (d) (15 points) Suppose we fix our P, rs, re as in (b), use curve() to plot A, and Ac in one graph. Label the x-axis as "Time, in Year , the y-axis as "Money, in Dollar. (e) (5 points) (Bonus) Are the two curves intersect with each other? if yes, can you find the intersection point? (f) (5 points) (Bonus) Can you use ggplot2 to plot part(d)