Natalie uses a credit card with a 23.6% APR, compounded monthly, to pay for a hotel stay totaling $748.12. She can pay $300 per month on the card. What will the total cost of this purchase be?

Question

anonymous · Answer

haha fun. Alright, so 23.6% APR (Annual Percentage Rate) compounded monthly will be paid off quickly with a $300 dollar payment. Wiki-page for compound interest http://en.wikipedia.org/wiki/Compound_interest The general formula looks like this: $$A(t)=A _{o} (1+r/n)^{[nt]}$$ t=time in years n=compounding periods per year (12 in your case since it's monthly) r=APR (expressed as a decimal i.e. 10% = .1) $$A _{o}$$ =principal amount $$A _{t}$$ =total amount So when we plug in your numbers. A(t)=748.12(1+.236/12) ^12 A(t)=748(1.0196666)^12 A(t)=748*1.263 = 944.724 or $944.73 The only thing I am kind of unsure of is her payments. I believe that they are irrelevant since you are using APR to calculate and the question asked what the total payment would be, not the total time it would take. You might have to extrapalate the equations on wiki 3 or 4 times to get a payment schedule and find a different number.

anonymous · Answer

Actually, now that I'm thinking more about it, I think that the 300 dollar payments is only included so that you can determine that she will pay it off in less than a year, and the total amount would be the same.

anonymous · Answer

thank you