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

Answer:

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

Step-by-step 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  × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

i.r A = P × $(1+\dfrac{\textrm r}{100})^{\textrm n}$

Or, A = 178,000 × $(1+\dfrac{\textrm 4.37}{100})^{\textrm 30}$

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 = $\dfrac{x}{100}$ × $642224

∴  $\dfrac{x}{100}$ =  $\dfrac{464224}{642224}$

∴  $\dfrac{x}{100}$ = 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