Mathematics
exyga356
19

Help please !! :( 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

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(1) Answers
Erasmo242

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. 

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