You are debating whether to buy a new computer for $1,360.00 with a discount of 10% and sales tax of
6.5% or a refurbished computer with the same equipment for $1,095.00 and sales tax of 5.75%. If a
savings account earns a 3.75% APR, how much do you really save with a refurbished computer if you put
the difference into the savings account for a year and calculate using the simple interest formula?
Be sure to include in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning

You want to know the amount saved by buying a refurbished computer for $1095 with 5.75% tax instead of a $1360 computer at a 10% discount with 6.5% tax, when the difference in purchase price earns 3.75% simple interest for a year.

New computer

The 10% discount means the price is multiplied by (1 -10%) = 0.90. The 6.5% tax means the discounted price is multiplied by (1 +6.5%) = 1.065. The net result is that the purchase cost of the new computer is ...

$1360 · 0.90 · 1.065 = $1303.56

Refurbished computer

Similarly, the tax multiplies the cost of the refurbished computer by 1.0575, so its cost is ...

$1095 · 1.0575 ≈ $1157.96

Savings

The difference between the costs is put into a savings account, so that will earn interest of 3.75%, bringing the balance to 1.0375 times the original savings:

($1303.56 -1157.96) · 1.0375 = $151.06

You really saved $151.06 if the original savings is put into a savings account.

__

Additional comment

The balance on an account earning simple interest at rate r for t years is ...

A = P(1 +rt)

Here, the amount put into the account is 145.60. At an interest rate of r=3.75%. In one year (t=1), this is multiplied by 1.0375 to obtain the "real savings."