Question

Matt Johnson takes out a mortgage for $240,000. There is a loan of 30 years at $1,200 per month. This gives a total interest of $192,000. What is the APR using the formula?

Answer 1

APR=((2×12×192,000)÷(240,000×361))×100
=5.32%

Answer 2

Answer:

The APR is 4.38%.

Step-by-step explanation:

Given : Matt Johnson takes out a mortgage for $240,000. There is a loan of 30 years at $1,200 per month. This gives a total interest of $192,000.

To find : What is the APR using the formula?

Solution : Formula of monthly payment  

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$  

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $240,000

Monthly payment  M=$1200

APR i =?

Time = 30 years  

$n=30\times12=360$

Monthly payment, $M=\frac{\text{A}}{\frac{1-(1+i)^{-n}}{i}}$  

$M=\frac{A\times i}{1-(1+i)^{-n}}$  

Substitute value,

$1200=\frac{240000\times i}{1-(1+i)^{-360}}$  

$\frac{1-(1+i)^{-360}}{i}=\frac{240000}{1200}$  

$\frac{1-(1+i)^{-360}}{i}=200$  

Solving using calculator,

$i=0.003655$

Now, In percentage and in months

$i=0.003655\times 100\times 12$

$i=4.38\%$

The APR is 4.38%.