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Lemur [1.5K]
3 years ago
6

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

Mathematics
1 answer:
cupoosta [38]3 years ago
8 0

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, <u>From Compound Interest method</u>

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

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