Annuity : yearly to monthly Kenton borrows $250,000 on January 1, 2012 to be repaid in 12 annual installments at an effective annual rate of interest of 12%. The first payment is due on January 1, 2013. Instead of annual payment he decides to make monthly payments equal to one-twelfth the annual payment beginning on February 1, 2013. Determine how many months will be needed to pay off the loan. (Ans : 129.381291) Anyone know how to solve this question?

Following that would be to use the annuity formula

$239641 = 3363*\dfrac{(1-\frac{1}{(1+r)^t})}{r}$

$\frac{1}{(1+r)^t} = 0.294671$ with r = 0.009489.

$(1+r)^t = 3.393617$

Taking log

$t \times ln(1.009489) = ln(3.393617)$

$t = \frac{ln(3.393617)}{ln(1.009489} = 129.3826$