Question

How much money should be deposited at age 5 in order to withdraw $50000 at the end of each year for 16 years if the first withdrawal is made at age 20. The account earns 9.5% compounded quarterly. Hint: Round effective rate to two decimal places. For the time where no withdrawals are being made, use 9.5% compounded quarterly.

Answer 1

To find the amount of money that should be deposited at age 5 in order to withdraw $50,000 at the end of each year for 16 years, we can use the formula for the present value of an annuity.

Step-by-step explanation:

To find the amount of money that should be deposited at age 5 in order to withdraw $50,000 at the end of each year for 16 years, we can use the formula for the present value of an annuity:

Present Value = (Payment / (1 + interest rate)^n) * ((1 - (1 / (1 + interest rate)^n)) / interest rate)

Using the given information, the payment is $50,000, the interest rate is 9.5% compounded quarterly (which translates to an effective annual rate of 9.5% * 4 = 38% compounded annually), and the number of periods is 15 (since the first withdrawal is made at age 20).

Plugging in these values, we can calculate the present value:

Present Value = ($50,000 / (1 + 0.38)^15) * ((1 - (1 / (1 + 0.38)^15)) / 0.38) = $50,000 / 24.7344532 * 4.68209002 = $78,902.99 (rounded to the nearest cent).