Question

Jerry and Dee have different opinions on how to save money. Jerry likes to have the highest possible amount withheld from his paycheck for their incomes taxes. That way, he knows he will not come up short and he loves getting a big tax refund each spring. When the refund comes, he deposits it into savings; he feels that is a less painful way to save.

Dee prefers to calculate monthly tax withholdings closer to the actual amount owed and deposit the extra cash (the difference between the highest possible amount and the amount they actually owe in taxes) into their savings account.

Last year, they followed Jerry’s method and received a tax refund check of $8,000 this year. Suppose instead they had followed Dee’s method.

a. If Jerry’s method yields an $8000 tax refund at the end of the year, how much would Dee have put away in savings every month instead? (Hint 8000 extra by the end of the year would be how much extra per month?)

b. How much would they have had at the end of the year if they followed Dee’s method and deposited the extra monthly amount into a savings account that pays 3% annual interest compounded monthly?

c. What is the difference if their account earns 6% compounded monthly?

d. Many people are excited when they get a big tax refund in the spring. Why do you suppose they over-withhold, even though they could earn more money by saving the money in an interest bearing account instead of letting the IRS hold onto it for free?

Answer 1

a)	Savings per month = 8000/12 =	$                667
b)	Amount in hand at the end of the year = 667*(1.0025^12-1)/(0.0025) =	$            8,115
	[Formula for finding FV of annuity is used; n = 12
	months and interest in decimals = 0.03/12 = 0.0025]
c)	Amount in hand at the end of the year = 667*(1.005^12-1)/(0.005) =	$            8,228
	[Formula for finding FV of annuity is used; n = 12
	months and interest in decimals = 0.06/12 = 0.005]
	Difference = 8228-8115 =	$                113
d)	They prefer to overwithold as the savings is automatic
	and they do not have to make deposits every month.
	Besides, they may prefer not to be short in tax payment
	at the end of the year, thereby having to pay a big
	amount in the end.
	Further, refund can be got only in the end of the year
	and there will be no temptation as in a savings account
	to withdraw it earlier.