Question

Sophia's credit has an APR of 20.87 % and it just changed its compounding. From monthly to daily what will happen to the effective interest rate charged to Sophia

Answer 1

Answer:

It will increase by 0.2%.

Step-by-step explanation:

In this problem we need to solve for the monthly interest first.

We use the formula:

$r = (1+\dfrac{i}{n})^{n}-1$

Now that we have the formula we now define our variables.

i = 20.87% or 0.2087

n = 12

$r=(1+\dfrac{0.2087}{12})^{12} - 1$

$r=(1+\dfrac{0.2087}{12})^{12}-1$

$r=(1+\dfrac{0.0174})^{12}-1$

$r=(1.0174})^{12}-1$

$r= 1.2299-1$

$r= 0.2299$ or 23%

Now we have to find the daily interest rate.

$r=(1+\dfrac{0.2087}{365})^{365}-1$

$r=(1+\dfrac{0.2087}{365})^{365}-1$

$r=(1+0.00057178082)^{365}-1$

$r=(1.00057178082)^{365}-1$

$r= 1.2320-1$

$r= 0.2320$ or 23.20%

23.20% - 23% = 0.20% increase.