Question

You want to be able to withdraw 540,000 from your account each year for 30 years after you retire. If you expect to retire in 20 years and your account earns 7% interest while saving for retirement and 5.5% interest while retired Round your answers to the nearest centar needed.

a) How much will you need to have when you retire
b) How much will you need to deposit each month until retirement to achieve your retirement goala?
c) How much did you deposit into you retirement account?
d) How much did you receive in payments during retirement?
e) How much of the money you received was interest?

Answer 1

a) The amount needed when you retire is $7,475,154.47. b) To achieve this retirement goal, you need to deposit $1,767.10 each month until retirement. c) You will need to deposit a total of $424,104 into your retirement account.

Step-by-step explanation:

To determine how much you will need for retirement, we can use the concept of future value of an annuity. In this case, the annuity is the annual withdrawal of $540,000 for 30 years. With an expected interest rate of 5.5% during retirement, we can calculate the amount needed:

a) The future value of the annuity is $540,000 * [(1+0.055)^30 - 1] / 0.055 = $7,475,154.47 rounded to the nearest cent.

b) To deposit a monthly amount to reach this goal, we can use the formula for the present value of an annuity: $7,475,154.47 = X * [1 - (1+0.07/12)^(-240)] / (0.07/12), where X is the monthly deposit. Solving for X gives us a deposit amount of $7,475,154.47 * (0.07/12) / [(1+0.07/12)^240 - 1] = $1,767.10 rounded to the nearest cent.

c) To find the total amount deposited into the retirement account, we can multiply the monthly deposit by the number of months until retirement: $1,767.10 * 12 * 20 = $424,104 rounded to the nearest cent.

d) The total payments received during retirement can be calculated by multiplying the annual withdrawal by the number of years: $540,000 * 30 = $16,200,000 rounded to the nearest cent.

e) To determine the amount of the money received that was interest, we subtract the total amount deposited from the total payments received: $16,200,000 - $424,104 = $15,775,896 rounded to the nearest cent.