Question

You want to be able to withdraw $20,000 each year for 15 years. Your account earns 8% interest.

A.) How much do you need in your account at the beginning?
B.) How much total money will you pull out of the account?
C.) How much of that money is interest?

Answer 1

To have $20,000 each year for 15 years with an 8% interest rate, you need $193,364.86 in your account at the beginning. The total money you will pull out of the account is $300,000, and $106,635.14 of that money is interest.

Step-by-step explanation:

A.) To determine how much you need in your account at the beginning, we can use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^n)] / r

Where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate, and n is the number of years.

In this case, PMT = $20,000, r = 8%, and n = 15.

Plugging in these values, we have:

PV = $20,000 * [(1 - (1 + 0.08)^15)] / 0.08

Solving this equation gives us the answer: $193,364.86.

B.) The total amount of money you will pull out from the account can be calculated by multiplying the annual withdrawal amount by the number of years: $20,000 * 15 = $300,000.

C.) The amount of that money that is interest can be calculated by subtracting the initial account balance from the total amount of money withdrawn: $300,000 - $193,364.86 = $106,635.14.