Question

John Blake takes out a mortgage for $80,000. There is a loan of 30 years at $600 per month. This gives a total interest of $136,000 for 30 years. What is the APR using the formula?

Answer 1

Answer: 8.4 %

Step-by-step explanation:

Since, the monthly payment formula,

$P = \frac{r(PV)}{1-(1+r)^{-n}}$

Where, PV is the present value of the loan,

r is the rate per period,

n is the number of periods,

Here, PV = $ 80,000

P = $ 600

n = 12 × 30 = 360

Let r be the annual rate ,

⇒  $600 = \frac{\frac{r}{12}\times 80,000}{1-(1+\frac{r}{12})^{-360}}$

⇒ $600 = \frac{\frac{80000r}{12}}{1-(1+r/12)^{-360}}$

⇒ $600(1-(1+\frac{r}{12})^{-360}) = \frac{80,000r}{12}$

⇒ $r = 0.082$

Thus, the annual rate of interest = 0.082 = 8.2 %

Answer 2

Hi there :-)

ARP IS
((2×12×136,000)÷(80,000×361))×100
=11.30%

HOPE IT HELPS