Problem and Program Details: With the help of an RESP (Registered Education Savings Plan), a parent can start putting aside money for a child's post-secondary education. Suppose that a young couple deposits $2,000 to start the savings plan, and each month thereafter they contribute $200. Assume that a fixed interested rate of 6% per year compounded monthly is applied. Each month the balance increases according to the following formula: New balance = Old balance + (Old balance * Monthly interest rate) + Monthly contribution (1) Since the university tuition fee increases over the years, you are asked to further analyze whether the saving is enough to cover the tuition fee for a 4-year study program. You will help them analyze this for 3 different types University programs: Arts, Science, and Engineering, for which the average tuition fees in the current year are as follows: $6000, $6500, and $7000 respectively. The predicted average percentage of tuition increase each year is 5.75%. Each year the new fee due to the annual increase is calculated as follows: New cost = Old cost + (Old cost * Annual increase rate) (2) Part A: In this part, you are asked to calculate the balance of the saving account in each month over 18 years, so the total saving by the end of the 18th year is known. Then calculate the predicted total tuition fee by the 18th year, which should be the total fee over a 4-year university program (i.e. from year 19 to year 22). A for loop can be used for the above calculations. Finally, by comparing the total savings and the predicted total tuition fee, determine whether or not the saving goal is achieved by the end of the18th year. Steps: 1. Calculate the monthly balance of the savings plan for the next 18 years, based on the formula in equation (1). Save the amount in a vector or an array. 2. Calculate the predicted tuition fee per year for the next 22 years, and then add up the fees over the last 4 college years (from the year 19 to year 22) to get the predicted total education cost for a 4-year program. 3. Compare the savings plan balance and the cost calculated from the step 2. Are the parents saving enough? Print the answer in the command window. To visualize the result, you are also asked to plot the annual savings with respect to the number of years; plot a horizontal line (threshold) indicating the total tuition fee on the same plot. Obviously, if the saving plot goes above this threshold at year 18, then the objective of the saving plan is achieved; otherwise, the objective is not achieved, the customer may choose to increase the monthly saving amount. Output: To summarize, in this part, your program needs to generate the following outputs: An answer to whether or not the parents are saving enough, in the command window; A plot showing both the plot of the annual savings vs. the years, and the threshold line (for the cost). Please label your plot properly. Sample Screenshots should look similar to the ones included. If it is successful ... If it is not successful ... Command Window Select a program: 1. Arts; 2. Science; 3. Engineering: At the end of 18 years you will have saved $ The cost of a 4-year college tuition fee is $ Congratulations!!!! You have saved enough. Command Window Select a program: 1. Arts; 2. Science; 3. Engineering: At the end of 18 years you will have saved $ The cost of a 4-year college tuition fee is $ The saving is $ short. fx >> Figure 1 BOX - Figure 1 File Edit View Insert Tools Desktop Window Help File Edit View Insert Tools Desktop Window Help Bad ADE - College Savings vs. Tuition fee College Savings vs. Tuition fee 12 14 16 2 4 6 12 14 18 8 10 Year 16 18 8 10 Year Note: The lines will cross The lines do not cross Problem and Program Details: With the help of an RESP (Registered Education Savings Plan), a parent can start putting aside money for a child's post-secondary education. Suppose that a young couple deposits $2,000 to start the savings plan, and each month thereafter they contribute $200. Assume that a fixed interested rate of 6% per year compounded monthly is applied. Each month the balance increases according to the following formula: New balance = Old balance + (Old balance * Monthly interest rate) + Monthly contribution (1) Since the university tuition fee increases over the years, you are asked to further analyze whether the saving is enough to cover the tuition fee for a 4-year study program. You will help them analyze this for 3 different types University programs: Arts, Science, and Engineering, for which the average tuition fees in the current year are as follows: $6000, $6500, and $7000 respectively. The predicted average percentage of tuition increase each year is 5.75%. Each year the new fee due to the annual increase is calculated as follows: New cost = Old cost + (Old cost * Annual increase rate) (2) Part A: In this part, you are asked to calculate the balance of the saving account in each month over 18 years, so the total saving by the end of the 18th year is known. Then calculate the predicted total tuition fee by the 18th year, which should be the total fee over a 4-year university program (i.e. from year 19 to year 22). A for loop can be used for the above calculations. Finally, by comparing the total savings and the predicted total tuition fee, determine whether or not the saving goal is achieved by the end of the18th year. Steps: 1. Calculate the monthly balance of the savings plan for the next 18 years, based on the formula in equation (1). Save the amount in a vector or an array. 2. Calculate the predicted tuition fee per year for the next 22 years, and then add up the fees over the last 4 college years (from the year 19 to year 22) to get the predicted total education cost for a 4-year program. 3. Compare the savings plan balance and the cost calculated from the step 2. Are the parents saving enough? Print the answer in the command window. To visualize the result, you are also asked to plot the annual savings with respect to the number of years; plot a horizontal line (threshold) indicating the total tuition fee on the same plot. Obviously, if the saving plot goes above this threshold at year 18, then the objective of the saving plan is achieved; otherwise, the objective is not achieved, the customer may choose to increase the monthly saving amount. Output: To summarize, in this part, your program needs to generate the following outputs: An answer to whether or not the parents are saving enough, in the command window; A plot showing both the plot of the annual savings vs. the years, and the threshold line (for the cost). Please label your plot properly. Sample Screenshots should look similar to the ones included. If it is successful ... If it is not successful ... Command Window Select a program: 1. Arts; 2. Science; 3. Engineering: At the end of 18 years you will have saved $ The cost of a 4-year college tuition fee is $ Congratulations!!!! You have saved enough. Command Window Select a program: 1. Arts; 2. Science; 3. Engineering: At the end of 18 years you will have saved $ The cost of a 4-year college tuition fee is $ The saving is $ short. fx >> Figure 1 BOX - Figure 1 File Edit View Insert Tools Desktop Window Help File Edit View Insert Tools Desktop Window Help Bad ADE - College Savings vs. Tuition fee College Savings vs. Tuition fee 12 14 16 2 4 6 12 14 18 8 10 Year 16 18 8 10 Year Note: The lines will cross The lines do not cross