Question 2 Scenario (Use for Part (a) to Part (d) in this question) You are planning to buy a house in four years' time and expect it to cost $1,000,000. You know you will need to make a downpayment of $100,000 at that time to acquire the house. Notes: You must show all workings. If there are no workings you will not get full marks even if the final answer is correct. Question 2(a) REQUIRED: If you have a savings account that pays interest of 6% per annum and compounds annually, how much money would you need to deposit in the savings account today so that you would have $100,000 available in 4 years' time? (Clearly show your workings, round to 2 decimal places and conclude with a concise statement detailing your final answer to the problem). (3 marks) Note: Enter your numerical answer in the designated places below. Do not put a dollar sign ($) in your numerical answers. Show your calculations (workings) in the box provided. Round your answer to two decimal places. Interest Factor Tables have been provided.
Question
Question 2 Scenario (Use for Part (a) to Part (d) in this question)
You are planning to buy a house in four years' time and expect it to cost 100,000 at that time to acquire the house.
Notes:
You must show all workings. If there are no workings you will not get full marks even if the final answer is correct.
Question 2(a)
REQUIRED:
If you have a savings account that pays interest of 6% per annum and compounds annually, how much money would you need to deposit in the savings account today so that you would have $100,000 available in 4 years' time? (Clearly show your workings, round to 2 decimal places and conclude with a concise statement detailing your final answer to the problem).
(3 marks)
Note:
Enter your numerical answer in the designated places below. Do not put a dollar sign ($) in your numerical answers. Show your calculations (workings) in the box provided. Round your answer to two decimal places. Interest Factor Tables have been provided.
Solution
To solve this problem, we need to use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, we are trying to find out the principal amount (P), so we need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
We know that A = $100,000, r = 6% or 0.06 (in decimal), n = 1 (since it compounds annually), and t = 4 years. Substituting these values into the formula, we get:
P = 100,000 / (1 + 0.06/1)^(1*4) P = 100,000 / (1.06)^4 P = 100,000 / 1.262476 P = $79,204.26
So, you would need to deposit 100,000 available in 4 years' time.
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