Question

Assume that you have graduated and have gotten a good job. You are conscientious and want to begin a savings account. You are paid monthly and have authorized your bank to automatically withdraw $300 from each paycheck. The bank made the first withdrawal on August 1, 2007 and you instruct them to make the last withdrawal on July 1, 2037. The withdrawals are invested at a nominal interest rate of 10% and compounded monthly. What will be the balance of the account on July 1, 2037

Answer 1

The balance of the account on July 1, 2037 will be $677,846.38.

Step-by-step explanation:

Since the withdrawals are made the beginning of each month, the relevant formula to use is the formula for calculating the Future Value (FV) of an Annuity Due is employed as follows:

FV = M * (((1 + r)^n - 1) / r) * (1 + r) ................................. (1)

Where,

FV = Future value or the balance of the account on July 1, 2037 =?

M = Monthly withdrawal = $300

r = Monthly interest rate = nominal interest rate / 12 = 10% / 12 = 0.10 / 12 = 0.00833333333333333

n = Number of months from August 1, 2007 to July 1, 2037 = 359

Substituting the values into equation (1), we have:

FV = $300 * (((1 + 0.00833333333333333)^359 - 1) / 0.00833333333333333) * (1 + 0.00833333333333333)

FV = $300 * 2,240.81447087212 * 1.00833333333333333

FV = $677,846.38

Therefore, the balance of the account on July 1, 2037 will be $677,846.38.