Question

Mary Smith took a car loan of $26,000 to pay back in 60 monthly installments at an interest rate of 12%.  
Compute the loan balance immediately after the 40th payment.

The answer choices are :

$11,567

$9,463  

$10,437

$13,000

I would rather you show me exactly how to solve this problem rather than just give an answer?

Answer 1

Option 3

First we need to find monthly EMI = 26000(A/P,1%,60) = 26000*((0.01*(1+0.01)^60)/(((1+0.01)^60)-1)) = $578.36

Next, after 40th payment, there would be 20 months balance which is calculated as, = 578.6*(P/A,1%,20) = 578.36* (((1+0.01)^20)-1)/(0.01*((1+0.01)^20)) = 10436.83

So, after 40th payment there would be a balance of $10437