Respuesta :
Answer:
The time taken to pay off the Mortgage amount is 216 months .
Step-by-step explanation:
Given as :
The mortgage value of home = p = $165,000
The time period of mortgage = t = 30 years = 30 × 12 = 360 months
The monthly payment amount = $1100
So, The payment amount in 360 months = $1100 × 360 = $396,000
i,e Amount paid after 30 years = A = $396,000
Rate of interest applied = r = 5.05%
Let The time taken to pay off mortgage amount = T years
Now, From compound Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm T}[/tex]
Or, $396,000 = $165,000 × [tex](1+\dfrac{\textrm 5.05}{100})^{\textrm T}[/tex]
Or, [tex]\dfrac{396000}{165000}[/tex] = [tex](1.0505)^{T}[/tex]
Or, 2.4 = [tex](1.0505)^{T}[/tex]
Taking power [tex]\dfrac{1}{T}[/tex] both side
Or, [tex](2.4)^{\frac{1}{T}}[/tex]= [tex]((1.0505)^{T})^{\frac{1}{T}}[/tex]
Now, Taking Log both side
So, Log [tex](2.4)^{\frac{1}{T}}[/tex] = Log 1.0505
Or, [tex]\dfrac{1}{T}[/tex] × Log2.4 = 0.0213
Or, [tex]\dfrac{1}{T}[/tex] × 0.380 = 0.0213
Or, T = [tex]\dfrac{0.380}{0.0213}[/tex]
Or, T = 17.84 ≈ 18 years
So, The time take= T = 18 × 12 = 216 months
Hence, The time taken to pay off the Mortgage amount is 216 months . Answer
