Rick has a credit card that charges 19% interest compounded monthly. What is the true annual rate of interest for Rick's credit card?
(1 + (0.19/12))^12 -1
= 20.7% A.P.R.
Ah, the wonders of finance! So, Rick's credit card charges him 19% interest compounded monthly? Well, let's do some math magic to find out the true annual rate of interest.
First, we need to figure out how much interest he would accrue in a month. Since it's compounded monthly, we can just take the 19% and divide it by 12. That gives us a monthly interest rate of approximately 1.58% (19 ÷ 12 = 1.58).
Now, we need to calculate the annual interest rate. Since there are 12 months in a year, we'll raise the monthly interest rate to the power of 12: 1.0158^12 = 1.2183.
To find the true annual rate of interest, we subtract 1 (since 1 represents no interest) and multiply by 100 to get a percentage: (1.2183 - 1) × 100 ≈ 21.83%.
So, the true annual rate of interest on Rick's credit card is approximately 21.83%. Keep an eye out for those sneaky credit card rates, they can be quite the jokers!
To find the true annual rate of interest for Rick's credit card, you need to convert the monthly interest rate to an annual rate.
Step 1: Convert the monthly interest rate to a decimal:
19% = 19/100 = 0.19
Step 2: Add 1 to the monthly interest rate:
1 + 0.19 = 1.19
Step 3: Raise the result to the power of 12 (as there are 12 months in a year) to account for compound interest:
(1.19)^12 = 1.0019^12 ≈ 1.2167
Step 4: Subtract 1 from the result and convert it to a percentage to find the annual interest rate:
1.2167 - 1 = 0.2167
0.2167 = 21.67%
Therefore, the true annual rate of interest for Rick's credit card is approximately 21.67%.
To find the true annual rate of interest for Rick's credit card, we need to consider the effects of compounding.
The stated interest rate of 19% is divided by the compounding periods in a year, which is 12 because it is compounded monthly. This gives us the monthly interest rate.
Let's calculate the monthly interest rate first:
Monthly interest rate = Annual interest rate / Number of compounding periods per year
= 19% / 12
= 0.19 / 12
= 0.01583 (rounded to 5 decimal places)
Now, to convert the monthly interest rate to an annual rate, we add 1 to the monthly interest rate, then raise it to the power of 12 (since there are 12 months in a year). We subtract 1 from the result, and finally, multiply it by 100 to express it as a percentage.
Let's perform the calculation:
Annual interest rate = ((1 + Monthly interest rate) ^ Number of compounding periods per year) - 1
= ((1 + 0.01583) ^ 12) - 1
= (1.01583 ^ 12) - 1
= 1.2059 - 1
= 0.2059 (rounded to 4 decimal places)
Therefore, the true annual rate of interest for Rick's credit card is approximately 20.59%.