1. ## Simple Annuities #2

Another question, i have the answer, but i am not sure if my working is the right working.

'A car loan of $10,000 at $J_{12}=12$% is being paid off by n monthly payments. The first (n-1) payments are$263.34 per month. The final payment is \$263.24.

Determine the duration of the loan.

What i did was:

$10000 = 263.34 \left[ \frac{1-(1+i)^{-n}}{i} \right]$

where $i= \frac{0.12}{12}$, and n= unknown. After simplification i get n=47.99

Is this working correct? I didn't include the n-1 or the final payment in my calculation, so I think I am wrong.