The APR is 24%, so the monthly rate is 24/12 = 2% which converts to the decimal form 0.02
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Problem 1
- After one month, the expression is 1000*(1.02)^1
- After two months, the expression is 1000*(1.02)^2
- After six months, the expression is 1000*(1.02)^6
- After twelve months or one year, the expression is 1000*(1.02)^12
Refer to problem 2 below. Note how only the exponent is changing. The 1.02 is from 1+0.02, which is in the form 1+r.
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Problem 2
In general, the balance after m months is 1000(1.02)^m
This formula is very similar to the compound interest formula.
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Problem 3
Computing 1000(1.02)^12 gets us 1,268.24179456254 approximately which rounds to 1,268.24
After 1 year, the cardholder owes $1,268.24
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Calculating the effective APR
r = APR = 0.24
s = effective APR
s = (1 + r/12)^12 - 1
s = (1 + 0.24/12)^12 - 1
s = 0.26824179456254
s = 0.2682
s = 26.82%
The effective APR is roughly 26.82%
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Problem 4
After t years, the balance will be approximately 1000*(1.2682)^t
The 1.2682 is from adding 1+0.2682, and the 0.2682 was the effective rate calculated in problem 3. The effective rate helps find the total amount of interest charged on a yearly basis. This assumes that no extra purchases were made and no payments were made either.
