A building is priced at 125,000. If a down payment of 25,000 is made and a payment of 1,000 every month thereafter is required, how many months will it take to pay for the building? Interest is charged at a rate of 9% compounded monthly.

Answer 1

P = (Po*r*t)/(1-(1+r)^-t)

Po = 125000-25000 = $100000.

r = (9%/12)/100% = 0.0075 = Monthly %
rate expressed as a decimal.

Po*r*t = 100000*0.0075t = 750t

P = 1000t.

P = 750t/(1-1.0075^-t) = 1000t
Divide both sides by 750t:
1/(1-1.0075^-t) = 1.333
Cross multiply:
1.333(1-1.0075^-t^-t) = 1
1-1.0075^-t = 0.750.
1.0075^-t = 1-0.75 = 0.25
-t*Log 1.0075 = Log 0.25
-t = Log 0.25/Log 1.0075 = -185.53
t = 185.53 Months.