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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(c) REQUIRED: Assuming the savings account in part (a) of this question still pays interest at 6% per annum compounded annually, how much will you need to deposit at the beginning of each year into the savings account, with the first deposit starting from today, to accumulate $100,000 in 4 years' time? (Clearly show your workings, round to 2 decimal places and conclude with a concise statement detailing your final answer to the problem). (4 marks) Note: Enter your numerical answer in the designated places below. Do not put a dollar sign ($) 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

You are planning to buy a house in four years' time and expect it to cost 1,000,000.Youknowyouwillneedtomakeadownpaymentof1,000,000. 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(c)

REQUIRED:

Assuming the savings account in part (a) of this question still pays interest at 6% per annum compounded annually, how much will you need to deposit at the beginning of each year into the savings account, with the first deposit starting from today, to accumulate $100,000 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).

                                                                                                                                                (4 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.

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Solution

To solve this problem, we need to use the formula for the future value of an annuity due, which is:

A = P * [(1 + r/n)^(nt) - 1] / (r/n) * (1 + r/n)

Where: A = the amount of money accumulated after n years, including interest. P = the amount of each payment (which we are trying to find) 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 payment amount (P), so we need to rearrange the formula to solve for P:

P = A * (r/n) / {[(1 + r/n)^(nt) - 1] * (1 + r/n)}

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 * (0.06/1) / {[(1 + 0.06/1)^(1*4) - 1] * (1 + 0.06/1)} P = 6,000 / {[(1.06)^4 - 1] * 1.06} P = 6,000 / {1.262476 - 1 * 1.06} P = 6,000 / 0.262476 P = $22,852.02

So, you would need to deposit 22,852.02atthebeginningofeachyearintothesavingsaccount,withthefirstdepositstartingfromtoday,toaccumulate22,852.02 at the beginning of each year into the savings account, with the first deposit starting from today, to accumulate 100,000 in 4 years' time.

This problem has been solved

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