[Maximum mark: 24) A teacher wants to invest money for the future by investing a regular amount. The investments eam compound interest at an annual interest rate. It is assumed that interest is compounded at the end of the compounding period. Give your answers correct to the nearest USD (United States Dollar). a) The teacher invests 1200 USD at a rate of 2% per year, added annually. i) Write a formula for the amount of money Ad) that the teacher has at the end of year 1. [2] [2] ii) Calculate the value of the investment after 4 years, showing your working. Ina iii) [4] Find the time taken for the investment to double. Write your answer in first in the exact form , a,b ER+ as well as Inb approximated to the nearest whole year. iv) The teacher decides to invest 1200 USD at 2% per year compounded annually every year for 25 years. Find the value of all of these investments at the end of the 25 years. Show all your working. V) Referring to the investment in part (iv), how many years would it take for the investments to have a total value of 50000 USD? s x a TSRS/DLF/181/2020-2021/P2 b) The teacher decides to buy a house for which a loan of 250000 USD is taken from the bank. The bank charges interest at the rate of 4% per year, compounded every six months at the end of each compounding period. The teacher will pay off the loan in monthly payments. i) If the teacher wants to pay off the loan in 30 years, what are the months monthly payments? Explain any queries that you make into your GDC, to calculate the payments. [3] What is the total amount that the teacher paid for the house at the end of the 30 years? [2] The teacher decides to increase the monthly payments by 10% compared to the answer found in part (b)(i) and agrees with the bank on a shorter period of repayment. Describe in detail, using appropriate calculations and/or technology, the effect of this change on paying off the loan