Question

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

that he has paid $240,141 towards the mortgage. What is the approximate APR?
APR = __2nf
R
P
(N+1)
3%
0
6%
0
0
7%

Answer 1

The Annual rate of interest for the mortgage is 1.8%

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

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

Or, $240,141 = $167,000 ×
`(1+(\textrm r)/(100))^(\textrm 20)`

or,
`(240,141)/(167,000)` =
`(1+(\textrm r)/(100))^(\textrm 20)`

Or , 1.437 =
`(1+(\textrm r)/(100))^(\textrm 20)`

Or,
`(1.437)^{(1)/(20)}` =
`(1+(r)/(100))`

or, 1.018 =
`(1+(r)/(100))`

Or,
`(r)/(100)` = 1.018 - 1

Or,
`(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