Sharon purchased a sprinkler system for $1,950 using a six-month deferred payment plan. The interest rate after the introductory period is 23.99%. No down payment is required, but there is a minimum monthly payment of $25. What is the balance at the beginning of the seventh month if only the minimum payment is made each month during the introductory period?

a.1950.00
b.2045.91
c.2195.91

(these answers are rounded to the fourth decimal place)
I was given this formula, but I can't figure it out: M=P(i(1+i)^nt / (1+i)^nt-1

Question

Sharon purchased a sprinkler system for $1,950 using a six-month deferred payment plan. The interest rate after the introductory period is 23.99%. No down payment is required, but there is a minimum monthly payment of $25. What is the balance at the beginning of the seventh month if only the minimum payment is made each month during the introductory period?
 
a.1950.00
b.2045.91
c.2195.91

(these answers are rounded to the fourth decimal place)
I was given this formula, but I can't figure it out: M=P(i(1+i)^nt / (1+i)^nt-1

anonymous · Answer

The correct answer is b, but I guessed. I would like to know how to get that answer.

mathstudent55 · Answer

Start with 1950
After 1st month: 1950 -25 = 1925
After 2nd month: 1925 - 25 = 1900
After 3rd month: 1900 - 25 = 1875
After 4th month: 1875 - 25 = 1850
After 5th month: 1850 - 25 = 1825
After 6th month: 1825 - 25 = 1800
Future Value = P(1 + i)^n = $1950(1 + 23.99/100/12)^6 = $2195.91
Interest = Future Value - Present value = 2195.91 - 1950 = $245.91
$1800 + $245.91 = $2045.91

directrix · Answer

@Iswimstar --> See discussion at http://openstudy.com/study#/updates/510dc843e4b0d9aa3c47828d