Answer:
426.62 payments
Step-by-step explanation:
You want to know the number of monthly payments it takes to pay off a loan of $290,000 at 4.7% interest with monthly payments of $1400.
Amortization
The formula for computing the monthly payment is ...
[tex]A=\dfrac{P\left(\dfrac{r}{12}\right)}{1-\left(1+\dfrac{r}{12}\right)^{-n}}[/tex]
where P is the principal amount of the loan at annual rate r for n payments.
Payments
Solving for n, we find ...
[tex]A-A\left(1+\dfrac{r}{12}\right)^{-n}=\dfrac{Pr}{12}\\\\\\1-\dfrac{Pr}{12A}=\left(1+\dfrac{r}{12}\right)^{-n}\\\\\\n=-\dfrac{\log{\left(1-\dfrac{r}{12}\cdot\dfrac{P}{A}\right)}}{\log{\left(1+\dfrac{r}{12}\right)}}=-\dfrac{\log0.1886905}{\log 1.0039167}\approx 426.615[/tex]
It will take 426.62 monthly payments.
