Question

You are starting medical school today. Becoming a doctor is your lifetime dream, so you started saving money when you were little. You now have $200,000 in your account, and you are going to withdraw annually starting today over the next four years. If you can earn 3 percent interest on the account, how much a year can you withdraw? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

Answer 1

$52,238.26

Step-by-step explanation:

Since he is going to withdraw annually starting today over the next four years, the formula to use to calculate how much to withdraw a year is the formula for annuity due.

Basically, annuity refers to financial investment that pays investors a fixed stream of amount for a specified period. It of two types: ordinary annuity that pays at the end of the period, and annuity due that pays at beginning of the period.

Since our focus here is annuity due, we employ the following annuity due formula:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] × (1+r) ....................................... (1)

Where

A

PV = Present value of an annuity due = $200,000

P = yearly withdrawal = ?

r = interest rate = 3% = 0.03

n = number of years = 4

Therefore, we have:

200,000 = P × [{1 - [1 ÷ (1+0.03)]^4} ÷ 0.03] × (1+0.03)

200,000 = P × [{1 - [1 ÷ (1.03)]^4} ÷ 0.03] × (1.03)

200,000 = P × [{1 - [1 ÷ 1.12550881]} ÷ 0.03] × (1.03)

200,000 = P × [{1 - 0.888487047915689} ÷ 0.03] × (1.03)

200,000 = P × [0.111512952084311 ÷ 0.03] × (1.03)

200,000 = P × 3.71709840281037 × 1.03

200,000 = P × 3.82861135489468

Rearranging, we have:

P = 200,000 ÷ 3.82861135489468

P = 52,238.26

Therefore, $52,238.26 can be withdrawn a year.