Answer:
the question is incomplete, so I looked for a similar one:
<em>Alex Karev has taken out a $180,000 loan with an annual rate of 11% compounded monthly to pay off hospital bills from his wife Izzy's illness. If the most Alex can afford to pay is $3,500 per month, how long will it take to pay off the loan? How long will it take for him to pay off the loan if he can pay $4,000 per month?</em>
PVIFA = $180,000 / $3,500 = 51.42857
PVIFA = [1 - 1/(1 + i)ⁿ ] / i = [1 - 1/(1 + 0.11/12)ⁿ] / 0.11/12
51.42857 x 0.11/12 = 1 - 1/(1 + 0.11/12)ⁿ
0.47143 = 1 - 1/(1 + 0.11/12)ⁿ
1/(1 + 0.11/12)ⁿ = 1 - 0.47143 = 0.52857
1 / 0.52857 = (1 + 0.11/12)ⁿ
1.89189 = 1.009167ⁿ
n = log 1.89189 / log 1.009167 = 0.2769 / 0.003963 = 69.87
n = 69.87 months
PVIFA = $180,000 / $4,000 = 45
PVIFA = [1 - 1/(1 + i)ⁿ ] / i = [1 - 1/(1 + 0.11/12)ⁿ] / 0.11/12
45 x 0.11/12 = 1 - 1/(1 + 0.11/12)ⁿ
0.4125 = 1 - 1/(1 + 0.11/12)ⁿ
1/(1 + 0.11/12)ⁿ = 1 - 0.4125 = 0.5875
1 / 0.5875 = (1 + 0.11/12)ⁿ
1.70213 = 1.009167ⁿ
n = log 1.70213 / log 1.009167 = 0.23099 / 0.003963 = 58.29
n = 58.29 months
