Question

Cathy takes out a $178,000 mortgage to be paid off over the span of 30 years. Cathy computers the APR at the end of the loan and determine it to be 4.37%.what is the percent of the total payment is interest

Answer 1

The interest of the mortgage is 72.2% of the total payment amount .

Explanation:

The principal mortgage amount = P = $178,000

Let The amount after 30 years = $A

The period for which money mortgage = n = 30 years

The rate at which money mortgage for 30 years = 4.37%

Let the interest is x % of the total payment amount

From Compound interest method

The amount after 30 years =The principal mortgage amount ×
`(1+(\textrm rate)/(100))^(\textrm time)`

i.r A = P ×
`(1+(\textrm r)/(100))^(\textrm n)`

Or, A = 178,000 ×
`(1+(\textrm 4.37)/(100))^(\textrm 30)`

Or, A = 178,000 ×
`(1.0437)^(30)`

Or, A = 178,000 × 3.6080

Or, A = $642224

So, The amount after 30 years = A = $642224

Now, Interest = Amount - Principal

Or, I = $A - $P

Or, I = $642224 - $178,000

∴ Interest = I = $464,224

So, The interest of the mortgage = I = $464,224

Now, Again

interest = x % of total payment amount

So, $464,224 =
`(x)/(100)` × $642224

∴
`(x)/(100)` =
`(464224)/(642224)`

∴
`(x)/(100)` = 0.722

i.e x% = 0.722

So, The interest is 72.2% of total payment

Hence,The interest of the mortgage is 72.2% of the total payment amount . Answer