Question

You are planning your retirement that will start at the age of 64. You currently are 30 years old. You think that you will live till you are 84 years old. You believe that to be able to live well during vour retirement years you will need $4500 per month In addition, you would like to have a car and a house. You would like to buy the car that will cost S30,000 when you turn 35, that is five years from today. You are currently living in a rented apartment. you want to purchase a house when you turn 50. The house you want to buy will cost $250,000. You realise that the goals you have set above are ambitious and might be difficult to attain. You have a rich uncle that has promised to give you an early inheritance in the amount of $100,000 when you turn 45 years old. You believe that this contribution from your uncle will be used to help meet your goals. The issue now is to determine how much you should deposit in the bank account you have opened to achieve the three objectives you set for yourself above. You believe that the bank will offer you a 12% APR under monthly compounding.

Answer 1

To achieve your retirement goals, you should deposit approximately $4,332,884 in your bank account.

Step-by-step explanation:

To determine how much money you should deposit in your bank account to achieve your retirement goals, we need to calculate the future value of your desired monthly income, the cost of the car, and the cost of the house.

To calculate the future value of your desired monthly income, we can use the formula:

FV = PMT * (((1 + r)^n - 1) / r),

• FV = Future Value
• PMT = Monthly Payment
• r = Annual Interest Rate / 12
• n = Number of Payments

Plugging in the values, we have:

FV = $4,500 * (((1 + 0.12/12)^(20*12) - 1) / (0.12/12)) = $2,156,204

Next, to calculate the future value of the car, we can use the same formula:

FV = PMT * (((1 + r)^n - 1) / r),

Plugging in the values, we have:

FV = $30,000 * (((1 + 0.12/12)^(5*12) - 1) / (0.12/12)) = $49,059

Finally, to calculate the future value of the house, we can use the same formula:

FV = PMT * (((1 + r)^n - 1) / r),

Plugging in the values, we have:

FV = $250,000 * (((1 + 0.12/12)^(14*12) - 1) / (0.12/12)) = $2,127,621

In order to achieve these goals, you should deposit a total of approximately $4,332,884 in your bank account.