Stefan wants to buy a stereo system that sells for $459.95 including taxes.

Question

Which plan should he choose to pay the least amount of money if he makes a down payment of $100 today?

 

Plan A: financing the remaining amount at 8% per year, simple interest, for two years.

Plan B: financing the remaining amount at 4% per year, simple interest, for 5 years.

Answer 1

Katie, here's the simple interest formula:

 

A = P(1 + rt)

 

P = 459.95 - 100 = 359.95

 

A = 359.95(1 + (.08 times 2)) = 359.95 (1.16) = 417.54

 

And,

 

A = 359.95(1 + (.04 times 5)) = 359.95 (1.20) = 431.94

 

So the shorter term, higher rate deal is better.

Answer 2

459.95 - 100 = $359.95

Plan A: i = prt

i = 359.95(.08)(2)

i = $57.59

 

Plan B: 

i = 359.95(.04)(5)

i = $71.99

 

Stefan should choose Plan A.

 

Answer 3

0.08(2) = 0.16

0.04(5) = 0.2

 

0.16 < 0.2, so A.