Question

You are going to make a substantial purchase. You have enough money to pay cash, but don’t know if that’s the way to make best use of your assets. Maybe you should take out an installment loan to make the purchase and invest the cash you would otherwise have used to pay for it.

Use the information provided to complete the following worksheet and analyze how the numbers work out most favorably for you. For simplicity, compounding is ignored in calculating both the cost of interest and interest earnings. [Note: Enter your dollar answers rounded to the nearest two cents and precede numbers that are less than zero (0) with a minus sign (–).]

Buy On Time or Pay Cash
Cost of Borrowing
1.	Terms of the loan
	a. Amount of the loan	$20,000
	b. Length of the loan (in years)	6
	c. Monthly payment	$322.00
2.	Total loan payments made
	($ per month months)		$
3.	Less: Principal amount of the loan		$
4.	Total interest paid over life of loan		$
5.	Tax considerations:
	– Is this a home equity loan?	no
	– Do you itemize deductions on your federal tax return?	yes
6.	What federal tax bracket are you in?	25%
7.	Taxes saved due to interest deductions
	($ x %)		$
8.	Total after-tax interest cost on the loan		$
Cost of Paying Cash
9.	Annual interest earned on savings
	(2% x )		$
10.	Annual after-tax interest earnings
	($ x %)		$
11.	Total after-tax interest earnings over life of loan
	($ x years)		$
Net Cost of Borrowing
12.	Difference in cost of borrowing versus cost of paying cash		$

Based on the numbers alone, you should      because:

If you invest the principal, you’ll earn more interest than you’ll pay on the loan.

The interest on a loan will cost you more than the interest you would earn if you invested the principal.

Answer 1

Calculating cost of borrowing

Loan amount = $20000, Length of Loan = 6 years = 6 x 12 = 72 months

Monthly payment= $322

Total loan payments made = Monthly payment x length of loan in months = 322 x 72 = 23184

Total interest paid over life of loan = 23184 - 20000 = 3184

Tax saved due to interest deduction = Federal tax bracket x total interest paid over loan = 25% x 3184 = 796

Total after tax interest cost of loan = Total interest paid over loan - Tax saved due to interest deduction = 3184 - 796 = 2388

Cost of paying cash

Annual interest earned on savings = loan amount x interest rate = 20000 x 2% =400

Annual after tax earnings = Annual interest earned on savings x (1 - federal tax bracket) = 400 x(1-25%) = 400 x 75% = 300

Annual after tax earnings over life of loan = Annual after tax earnings x life of loan in years = 300 x 6 = 1800

Calculating Net cost of borrowing

Net cost of borrowing = Difference between cost of borrowing and cost of paying cash = 2388 - 1800 = 588

Since the interest paid on loan is more that interest earned on investing the cash, hence one should pay cash.

We can also see that

If one takes the loan then Net profit = Interest earned on investment - interest on loan = 1800 - 2388 = -588

If makes cash payment then net profit = amount saved on loan - interest forgone on investment = 2388 - 1800 = 588

Therefore

Based on the numbers alone, you should pay cash because The interest on a loan will cost you more than the interest you would earn if you invested the principal.

	Buy On Time or Pay Cash
Cost of borrowing
1	Terms of loan
	a. Amount of Loan	20000
	b. Length of Loan (in years)	6
	c. Monthly payment	322
2	Total Loan Payments made
	($ per month months)	23184
3	Less: Principal amount of Loan	20000
4	Total Interest Paid over Loan	3184
5	Tax considerations
	Is this a Home equity loan	No
	Do you itemize deductions on Federal tax return	Yes
6	What federal tax bracket are you in	25%
7	Tax saved due to interest deductions
	($ x %)	796
8	Total after tax interest cost of loan	2388
Cost of Paying cash
9	Annual interest earned on savings
	(2% x )	400
10	Annual after tax earnings
	($ x %)	300
11	Total after tax earnings over life span
	($ x years)	1800
Net Cost of borrowing
12	Difference in cost of borrowing cost of paying cash	588