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nathan uses a credit card with a 20.4% apr, compounded monthly, to pay for a cruise totaling $1,045.87. he can pay $490 per month on the card. what will the total cost of this purchase be?
a. $1,045.87
b. $1,074.99
c. $1,140.86

The annual interest rate is 20.4% which is a 20.4/12 = 1.7% monthly rate.

1.7% = 0.017



Month 1:

interest = 0.017*(current balance)

interest = 0.017*(1045.87)

interest = 17.77979

interest = 17.78



principal = payment - interest

principal = 490 - 17.78

principal = 472.22



new balance = (old balance) - principal

new balance = (1045.87) - 472.22

new balance = 573.65

at the end of month 1, the balance is $573.65

So far, you have paid $490



Month 2:

interest = 0.017*(current balance)

interest = 0.017*(573.65)

interest = 9.75205

interest = 9.75



principal = payment - interest

principal = 490 - 9.75

principal = 480.25



new balance = (old balance) - principal

new balance = (573.65) - 480.25

new balance = 93.40

At the end of month 2, the balance is $93.40

So far, you have paid 490+490 = 980 dollars



Month 3:

The current balance of $93.40 is less than $490, so we don't have to pay the full $490. We can simply pay off the remaining balance. 

Add this to the current total paid amount so far to get 980+93.40 = 1,073.40

I'm not sure if I made a rounding error somewhere or if there is a typo. The closest answer choice I see is choice B. So I'm thinking the answer is choice B. I'd get a second opinion or ask the teacher on this one. 

Ibelieve it is