Question

Nicholas uses a credit card with a 19.1% APR, compounded monthly, to pay for a cruise totaling $2,513.69. He can pay $910 per month on the
card. What will the total cost of this purchase be?

Answer 1

is the credit card his?

Answer 2

Yes

Answer 3

We have 19.1% APR, which is the annual rate
What is the monthly rate?

Answer 4

$2.993.80
$2,513.69
$3,285.64
$2,591.95 these are the choices it gives

Answer 5

hint:
monthly rate = (APR)/12

Answer 6

So 910=(.191)/12

Answer 7

?

Answer 8

what does your calculator say when you type in 0.191/12

Answer 9

0.015

Answer 10

I'm getting 0.01591666666667
Let's round that to 0.0159167 just to keep things relatively simple

Answer 11

now multiply that with 2,513.69 and tell me what you get

Answer 12

40.0095658

Answer 13

I'm getting the same. Let's round that to 40.01 since money is usually rounded to the nearest cent (hundredth)

Answer 14

Okay

Answer 15

The 40.01 is the amount of interest for the month
The balance 2513.69 jumps up to 2553.70 after we add on the 40.01

In other words,
2513.69+40.01 = 2553.70

Answer 16

So we started with a balance of 2513.69 and now the balance is 2553.70

Answer 17

Correct

Answer 18

Then the payment of $910 will lower the balance to 2553.70-910 = 1643.70

With me so far?

Answer 19

Yes

Answer 20

ok that was all for month #1

Answer 21

we will repeat this process for month #2

Answer 22

start with a balance of 1643.70 and find the monthly interest you'll pay

So you'll need to multiply 1643.70 with 0.0159167

Answer 23

26.16227979

Answer 24

that rounds to 26.16

Answer 25

Add that onto the balance and you get what?

Answer 26

1,669.86?

Answer 27

correct

Answer 28

now subtract off the monthly payment of $910

Answer 29

759.86

Answer 30

correct

we'll need to do one more round of this

Answer 31

Ok

Answer 32

if the balance is 759.86, what is the monthly interest we pay for month #3?

Answer 33

How do I get that

Answer 34

multiply 759.86 with the value 0.0159167

Answer 35

since 0.0159167 was the monthly rate (in decimal form)

Answer 36

monthly interest = (current balance)*(decimal form of monthly rate)

Answer 37

Multiply by 759?

Answer 38

759.86 * 0.0159167 = ??

Answer 39

12.09

Answer 40

yes, so the balance goes from 759.86 to 759.86+12.09 = 771.95
Agreed?

Answer 41

Yes

Answer 42

At this point, we would subtract off the payment of $910
However, this payment is larger than the current balance
So we can just pay off the entire balance and bring it to 0
This means the final payment is $771.95 instead of $910

Answer 43

Throughout this process, you should be keeping track of all the values in a chart like you see below

Answer 44

Oh okay

Answer 45

The table is handy to see how much you pay on a given month, and what your balance is, etc

Answer 46

what do you get when you add up the stuff in the "payment" column?

Answer 47

So add everything?

Answer 48

just in the payment column

Answer 49

doing so will lead to the total cost, since it's the sum of all the payments

Answer 50

2,591.95

Answer 51

correct

Answer 52

so the answer is choice D

Answer 53

Thank you

Answer 54

If you're curious about the total interest paid, then you subtract the total cost and cost of the product
2591.95 - 2513.69 = 78.26

The total interest is $78.26

Answer 55

no problem