Question

Sam takes out a $167,000 mortgage for 20 years. He makes monthly payments and at the end calculates

Answer 1

Answer:

The Annual rate of interest for the mortgage is 1.8%

Step-by-step explanation:

Given as :

The mortgage principal = p = $167,000

The time period of mortgage = t = 20 years

The Amount paid towards mortgage in 20 years = A = $240,141

Let the Annual percentage rate on interest = r % compounded annually

Now, From Compound Interest method

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $240,141 = $167,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

or, $\dfrac{240,141}{167,000}$ =  $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or , 1.437 =  $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or, $(1.437)^{\frac{1}{20}}$ = $(1+\dfrac{r}{100})$

or, 1.018 = $(1+\dfrac{r}{100})$

Or, $\dfrac{r}{100}$ =  1.018 - 1

Or, $\dfrac{r}{100}$ = 0.018

∴ r = 0.018 × 100

i.e r = 1.8

So, The rate of interest applied = r = 1.8 %

Hence, The Annual rate of interest for the mortgage is 1.8%  Answer