Question

Dale has purchased a $165,000 home with a 30-year mortgage at 5.05%. He can make a monthly payment of $1100. If he were to make this payment each month, how long will it take him to pay off his mortgage?

A.
243 months

B.
237 months

C.
300 months

D.
217 months

Answer 1

Answer:237 months

Step-by-step explanation:

Answer 2

The time taken to pay off the Mortgage amount is 216 months .

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 ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, A = p ×
`(1+(\textrm r)/(100))^(\textrm T)`

Or, $396,000 = $165,000 ×
`(1+(\textrm 5.05)/(100))^(\textrm T)`

Or,
`(396000)/(165000)` =
`(1.0505)^(T)`

Or, 2.4 =
`(1.0505)^(T)`

Taking power
`(1)/(T)` both side

Or,
`(2.4)^{(1)/(T)}`=
`((1.0505)^(T))^{(1)/(T)}`

Now, Taking Log both side

So, Log
`(2.4)^{(1)/(T)}` = Log 1.0505

Or,
`(1)/(T)` × Log2.4 = 0.0213

Or,
`(1)/(T)` × 0.380 = 0.0213

Or, T =
`(0.380)/(0.0213)`

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