Nathaniel want to buy a new bike. His payment options are:

Question

Option 1: Pay $2055.99 cash. He only has $400.00 saved up, so he can take out a loan for the rest from his bank at a rate of 7.25% per annum over 2 years.
Option2: Take the store payment plan of 12 monthly payments of $180.00.
A.) If he chooses option 1, what will his monthly payment be?
B.) If he chooses Option 2, what annual rate of interest will he pay?
C) Calculate the total cost of each option. Which option should he choose, and why?

Answer 1

Assuming simple interest:
A. Po = 2055.99-400 = 1655.99
P = Po + Po*r*t
P = 1655.99 + 1655.99*0.0725*2
P = 1655.99 + 240.12 = $1896.11

1896.11/24mo = $79.00/Mo.

B. P = 180/mo * 12mo = $2160.

r = (p-Po)/Po = (2160-2055.99)/2055.99 =
0.0506 = 5.06% Per annum

C. Option 1: $1896.11
Option 2: $2160

He should choose option 1, because the
total cost and monthly payments are less,

Answer 2

Everything Henry calculated is correct until question C as the answer doesn't take into account the additional $400 down payment Nathaniel put towards the bike initially.
Total cost for option 1: $1896.11 + 400 = $2296.11
Option 2 is better