Question

A couple decides to buy a house which is currently valued at $318,921.46 on loan. The couple is willing to start paying $200.00 per month and are willing to increase their payment at a rate of 5% every month. How many payments are necessary to pay off the loan amount assuming no deposit was made (answer to the nearest whole number)? What is the value of the final payment that they would make assuming no deposit was made (answer to the nearest whole number)?

Answer 1

1. We solve by the formula of geometric progression:

$Sn=\frac{b1(q^n-1)}{q-1}$

Sn=$318,921.46

b1=200

q=1,05

$318921.46=\frac{200(1.05^n-1)}{1.05-1}$

$318921.46=4000(1.05^n-1)$

$1.05^n-1=79.73$

$1.05^n=80.73$

n=log_1.0580.73

n=89,99999

90 payments are necessary to pay off the loan amount assuming no deposit was made

2.Find the last member of the progression:

$bn=b1\times1.05^{n-1}$

$bn=200\times1.05^{90-1}$

$bn=200\times1.05^{89}$

bn=15 377.21=15378