# Math Help - Geometric progression

1. ## Geometric progression

anyone can understand this question??

a house buyer borrows rm50k from a bank to buy a house which costs rm70k. the rate of interest charged by the bank is 9% per annum, and is calculated based on the amount outstanding at the beginning of each year.the house buyer is required to repay his loan in monthly instalments for a period of 15 years. assuming that the rate of interest is fixed for the entire duration of the loan, find the amount per month he has to repay the bank

answer given :rm516.92 . math topic :geometric progression

2. Originally Posted by qweiop90
anyone can understand this question??

a house buyer borrows rm50k from a bank to buy a house which costs rm70k. the rate of interest charged by the bank is 9% per annum, and is calculated based on the amount outstanding at the beginning of each year.the house buyer is required to repay his loan in monthly instalments for a period of 15 years. assuming that the rate of interest is fixed for the entire duration of the loan, find the amount per month he has to repay the bank

answer given :rm516.92 . math topic :geometric progression
let the monthly repayument be $x$, then the amount repaid in a year is $12x$.

So if $p_1$ is the oustanding debt at the start of a year the outstanding debt at the start of the following year is:

$p_2=(p_1-12x) 1.09$

The next year:

$
p_3=(p_2-12x) 1.09=p_1 1.09^2-12x 1.09^2-12x 1.09
$

Proceeding in this way the debt after 15 years is:

$
p_{15}=p_1 1.09^{15} - \sum_{i=1}^{15} 12x 1.09^i=p_1 1.09^{15} - 12x \sum_{i=1}^{15} 1.09^i
$

CB