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 (so the interest rate is 5% monthly).

Using the geometric sequence formula, 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)First Monthly Payment = $ 200

Next payment rate = 1+5% = 1.05

Loan Amount = $318,921.46

Loan Amount = (First Monthly Payment*(1-next payment rate)^n)/(1-next payment rate)

$318,921.46 = (200(1-1.05)^n)/(1-1.05)

1-(1.05)^n= (318921.46 * -.05)/200

-(1.05)^n= - 79.730365 - 1

(1.05)^n = 80.7304

n=Log1.05(80.7304)

n=89.82 =90 months

90 payments required to pay off the loan

2) Monthly final Payment = Monthly first payment * (next payment rate)^(n-1)

Monthly final payment = 200*(1.05)^(90-1)

= 200*(1.05)^89

=200*76.886

=$15,377.21

$15,377 is the final payment they will made