Math question

Question

Brady needs to borrow $4500 to buy a car. he can borrow the money at a rate of 7.5% per year compounded monthly or at 8.25% per year simple interest. he must repay the loan after three years which option should she chose ? 

Answer 1

Compound interest:  A = P(1+r/n)^nt

 

A = 4500(1 + .075/12)¹²⁽³⁾ = 4500(1.00625)³⁶ = $5631.51

 

Simple Interest:  A = P(1+r)ⁿ

 

A = 4500(1.0825)³ = $5708.1

 

The final value of the loan is smaller with the compound interest

at 7.5% compounded monthly. 

 

the answer is option 1.

Answer 2

Option 1 - compound interest - amount payable = 4500 (1 + 7.5/1200)³⁶ = 5631.5

Option 2 - simple interest - amount payable = 4500 (1 + 3x8.25/100) = 5613.75

He should go with option 2.