You want to be able to withdraw $20,000 from your account each year for 15 years after you retire. If you expect to retire in 20 years and your account earns 7.4% interest while saving for retirement and 4.8% interest while retired:
Round your answers to the nearest cent as 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 goals?
$
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?
$
To determine the answers to these questions, we can use the concept of compound interest and annuity.
a) To find out how much you will need to have when you retire, we can calculate the future value of an annuity. The formula to calculate the future value of an annuity is:
FV = P * (1 + r)^n - 1 / r
Where:
FV = Future value of the annuity
P = Annual withdrawal amount ($20,000)
r = Interest rate before retirement (7.4% or 0.074)
n = Number of years in retirement (15)
Using the formula, we can calculate the future value of the annuity:
FV = $20,000 * (1 + 0.074)^15 - 1 / 0.074
Calculating this, the future value comes out to be: $316,854.86, which is the amount you will need to have when you retire.
b) To calculate how much you need to deposit each month until retirement, we can use the concept of present value of an annuity. The formula to calculate the present value of an annuity is:
PV = P * (1 - (1 + r)^-n) / r
Where:
PV = Present value of the annuity (amount you need to deposit each month)
P = Annual withdrawal amount ($20,000)
r = Interest rate before retirement (7.4% or 0.074)
n = Number of years until retirement (20)
Calculating this, the present value comes out to be: $15,497.45, which is the amount you need to deposit each month until retirement to achieve your retirement goals.
c) To calculate how much you deposited into your retirement account over the years, we can multiply the monthly deposit by the number of months in 20 years.
Total deposit = Monthly Deposit * Number of months
Using the value of $15,497.45 from the previous calculation, the total deposit comes out to be: $371,938.80.
d) To calculate how much you received in payments during retirement, we can multiply the annual withdrawal amount by the number of years in retirement.
Total payment = Annual withdrawal amount * Number of years in retirement
Using the value of $20,000 and 15 years, the total payment comes out to be: $300,000.
e) To calculate how much of the money you received was interest, we can subtract the total deposit from the total payment.
Interest received = Total payment - Total deposit
Using the values calculated previously, the interest received comes out to be: $300,000 - $371,938.80 = -$71,938.80.
Note that the negative value indicates that the total payments received during retirement were less than the total deposits made, meaning that part of the money came from the original deposits.