Answer to Question #291466 in Financial Math for Julia

Question

Mae purchased a home for ₱4,570,000 and obtained a 20-year loan with an annual interest rate of 8.5%, after paying a down payment of 25%. Find the the amount of interest paid on the loan over the 20 years

Answer 1

$P\ =\frac{A\left(\frac{r}{n}\right)}{{1\ -\ \left(1\ +\ \frac{r}{n}\right)}^{-nt}}$

$where\ A\ =\ \frac{25}{100}\ \times\ 4,570,000\ =\ 1,142,500$

$where\ r\ =\ \frac{8.5}{100}\ =\ 0.085$

$t\ =\ 20years$

$n\ =\ 12\ months$

$P\ =\frac{1,142,500\left(\frac{0.085}{12}\right)}{{1\ -\ \left(1\ +\ \frac{0.085}{12}\right)}^{-12\times20}}$

$P\ =\frac{8,092.708}{1\ -\ \left(0.1838\right)}$

$P\ =\ 9,915.10$

$The\ amount\ of\ interest\ paid\ on\ the\ loan\ over\ 20years\ will\ be\ \ ₱9,915.10$