The sum that Rodney owes after 1 year is $1811.70. This means that he has to pay $1811.70 to the credit card provider after 1 year.
The formula to calculate the sum due after a specified period when the interest is compounded monthly is:
[tex]\rm A = P( 1 + \dfrac{r}{n})^{nt}[/tex] , where A is the amount after compounding, P is the principal, r is the rate of interest, n is number of months and t is the tenure.
Given:
Principal(P) is $1,541.05
Annual percentage rate(APR/r) is 16.29%
Compounding is done monthly for 1 year. Therefore,
n is 12 and t is 1.
On substituting the values in the formula:
[tex]\rm A = P( 1 + \dfrac{r}{n})^{nt}\\ \\ A=1541.05(1+\dfrac{0.1629}{12})^{12(1)}\\ \\ A&=1541.05(1.013575)^{12}\\ \\ A=1541.05(1.17556)\\ \\ A=\$1811.70[/tex]
Therefore the amount Rodney owe after 1 year is $1811.05.
Learn more about compound interest here:
https://brainly.com/question/25857212
