Naomi uses a credit card with a 25.9% APR, compounded monthly, to pay for a hotel stay totaling $971.20. She can pay $400 per month on the card. What will the total cost of this purchase be?

Question

anonymous · Answer

Graph her costs monthly by starting at $971.20 and increasing it 25.9/12=2.16% each  month. Graph her payments at P = 400 x on the same graph, find how many months, see what the total cost is there.

Alternatively, solve (971.20)(1+.0216)^m - 400 m = 0

to get the number of months and thus the cost. m may not be simple number, but (971.20)(1+.0216)^m and a calculator should work.