Question

Grant's credit card has an apr of 11.28% and it just changed its compounding period from monthly to daily . What happen to the interest rate charged to grant

Answer 1

Changing the compounding period from monthly to daily generally results in a higher amount of interest paid over time because Grant's balance will accumulate interest at a slightly higher rate each day. To calculate the new interest payments, the daily interest rate is used, which is the APR divided by 365.

Step-by-step explanation:

When Grant's credit card APR (Annual Percentage Rate) changed its compounding period from monthly to daily, the effect on the interest charged to Grant would depend on how the daily rate is calculated. The APR is the annual rate of interest without taking into account the compounding of interest within that year. When interest is compounded more frequently, such as daily rather than monthly, it results in a higher amount of interest paid over the year because interest is being calculated on a slightly higher balance each day. To find the daily interest rate, you would divide the APR by 365 (the number of days in a year). This daily rate is then applied to the balance each day, resulting in daily compound interest.

To calculate the impact, one would use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.

By increasing the frequency of compounding, Grant will likely see a slight increase in the total amount of interest charged over time, assuming he carries a balance on his credit card.

Answer 2

C. It will increase by about 0.6%

Step-by-step explanation:

Since, the effective interest rate is,

`r=(1+(i)/(n) )^(n) -1`

Where, i is the stated interest rate,

n is the number of compounding periods,

Here, i = 11.28 % = 0.1128,

n = 365 ( 1 year = 365 days ),

Hence, the effective interest rate would be,

`r=(1+(0.1128)/(365))^(365) -1`

=0.119388521952

Now, the changes in effective interest rate = Effective interest rate - Stated interest rate

= 0.119388521952 - 0.1128

= 0.006588521952 ≈ 0.006 = 0.6 %

Hence, It will increased by about 0.6 %,

Option A is correct.

Hope this helps :)