Question

without using a financial calculator or excel. Please provide all formula used and variables with clear steps

Question 8 The rate of interest earned in a bank's savings account is 8% per annum effective (compound). Assume that there is no tax, no fees. John makes a deposit of $100 at time t = 0, and a deposit of $200 at time t = 1 year. (8)(a) What is the account balance at t = 8 years, after interest has been paid, assuming John has not made any withdrawal? [1 mark] (8)(b) What is the account balance at t = 8 years, after interest has been paid, if we know that John has withdrawn $300 from his account at t = 6 years? [1 mark] (9) Please write your answer in the answer book provided. Show your workings. Circle your final answer. The Bank charges annual effective rate of interest i = 10% on its home loans. Mary takes out a home loan of $1,000,000 from this Bank. (9)(a) Mary plans to make payments of $X at the end of each year for 30 years. Find the value of X. [1 mark] (9)(b) Mary plans to make payments of $Y at the end of each month for 30 years. Find the value of Y. (1 mark] (9)(c) Mary plans to make payments of $10,000 at the end of each month how long will it take for her to pay the loan? [1 mark]

Answer 1

8. a) The account balance at the end of 8 years would be equal to the future value of all investments less the future value of all withdrawals

So,

Account balance = 100*(1+0.08)^8 + 200*(1+0.08)^7 = $ 527.86

b) In this case

Account balance = 100*(1+0.08)^8 + 200*(1+0.08)^7 - 300* (1+0.08)^2 = $ 177.94